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Several algorithms are presented for solving the non-linear programming problem, based on “variable-metric” projections of the gradient of the objective function into a local approximation to the constraints. The algorithms differ in the nature of this approximation. Inequality constraints are dealt with by selecting at each step a subset of “active” constraints to treat as equalities, this subset being the smallest necessary to ensure that the new point remains feasible. Some numerical results are given for the Colville problems.

Cornell, like most other large schools, has been struggling with the problem of introductory programming instruction for years. The problem is not yet solved but in the last few years we have done some experimenting and seem to have made some progress. The situation seems worth reporting so that others can perhaps benefit from what has been successful and avoid what has not. The major problems seem to be volume and variety . Pedagogical techniques that are obviously effective with small classes are sometimes impractical when faced with more than a thousand students per year. This may be largely a question of economics, since one could presumably allocate enough resources to the task to have small classes, but this is just not realistic at Cornell and the real question becomes one of finding practical large-scale techniques. For example, the central computing facility at Cornell (a 360/65 under OS/HASP) cannot support a sufficient number of interactive terminals to make that mode of instruction practical. Hence our solution must operate within the constraint of a conventional non-inter-active computer service.

In this paper, we propose an integer quadratic optimization model to determine the optimal decision for a supplier selection problem. The decision is the optimal product volume that has to be purchased from each supplier so that the total cost is minimum and the constraints are satisfied. The cost function that we used is containing the purchasing cost, transportation cost, penalty cost for product that not satisfy the quality level, penalty cost for product that is late and the holding cost whereas the constraints are consisting of supplier capacity constraint, demand satisfying, supplier assignment, inventory management, and budget constraint. A numerical experiment with generated random data is given to illustrate how the supplier selection problem can be solved by using the proposed mathematical model. From the results, the optimum product volume from each suppliers was determined so that the total cost is minimum.

The problem of representation and handling of constraints is here considered, mainly for picture processing purposes. A systematic specification and utilization of the available constraints could significantly reduce the amount of search in picture recognition. On the other hand, formally stated constraints can be embedded in the syntactic productions of picture languages. Only binary constraints are treated here, but they are represented in full generality as binary relations. Constraints among more than two variables are then represented as networks of simultaneous binary relations. In general, more than one equivalent (i.e., representing the same constraint) network can be found: a minimal equivalent network is shown to exist, and its computation is shown to solve most practical problems about constraint handling. No exact solution for this central problem was found. Anyway, constraints are treated algebraically, and the solution of a system of linear equations in this algebra provides an approximation of the minimal network. This solution is then proved exact in special cases, e.g., for tree-like and series-parallel networks and for classes of relations for which a distributive property holds. This latter condition is satisfied in cases of practical interest.

The generalized von Neumann model of an expanding economy permits both joint products and alternative processes. Pollutants may be explicitly treated as the normal by-products of certain economic processes and “clean” and “dirty” production alternatives may be simultaneously available. The paper describes some methods for incorporating pollutants in the model and several techniques that may be used to study the relationship between pollution abatement and economic growth. Numerical examples are used to illustrate cases of direct control of processes, consumer demand for “eliminated pollutant” and the limitation of total produced pollutants by exogenous constraint. In the last case an effluent charge is calculated.

This paper discusses the roles of ecological and economic information in the political and legal matrix of international fisheries. An argument is made for vesting exclusive management authority in a monopoly subject to a constraint that stocks not be depleted beyond the point of economic restitution. It is suggested that an appropriate authority be chosen by the criterion of the closest merging of ecological, economic, sociological, and political self‐interests. The reallocation of fishing effort by market dealings rather than by governmental negotiations is visualized as a means to reduce international conflicts over fishing rights. Precedents for the various elements of this model and the dangers inherent in it are discussed.

Summary This article examines the causes and effects of the rapid rise and fall in prices in the United Kingdom's import market for butter during the years 1970 to 1972. A simple model is set up to show the workings of the market under quotas during the years 1967 to 1969. This model is used to test whether there is any difference in the structural operation of the market when the constraint is removed The interrelationship between the prices of butter from the various exporters to the U.K. is explored and implications for the effects of price rises entailed by the adoption of the EEC's Common Agricultural Policy are drawn.

This paper describes a planning model developed for an English local authority to help take into account the constraint of limited financial resources associated with physical planning decisions such as slum clearance, housing development and town centre redevelopment. Physical planning assumptions and decision inputs are incorporated into a model of the local authority environment having as major variables population, housing and employment. Each of the local authority services is represented separately and the majority are functions of these key variables. Service levels, where possible, and expenditures are projected and compared with a total resources projection to determine overall financial viability. Examples of the model's application are given.

In the Transportation Routing Problem, a manager or analyst must schedule an existing fleet of vehicles, each with a capacity constraint, to visit a set of stops or destinations and deliver or pick up goods or services at each stop such that one and only one vehicle visits each stop. The problem is to assign these vehicles to the stops so as to minimize total cost which is assumed to be directly proportional to the total distance traveled. Much work has been done on this problem and heuristic as well as optimal seeking methods have been developed. This paper examines the problem, develops a standard formulation, reviews the literature on the problem, and mentions some new approaches.

How a system of corrective taxes can be applied to the problem of managing surface water nitrate pollution in agricultural regions is demonstrated. A spatial linear programming model of the US livestock-feed complex including constraint equations linking fertilizer nitrogen use by Illinois farmers to water quality in that state has been developed. The solution to this model at various desired levels of NO/sub 3/-N in Illinois provides estimates of regional taxes on fertilizer nitrogen use appropriate to the ''Environmental Pricing and Standards'' system. In addition, other estimated changes in agricultural activity induced by this system of corrective taxes are presented. 20 references, 6 figures, 11 tables.

In this paper a simulation study of the effects of labor flexibility on the performance of a multiechelon dual-constraint job shop is described. Machines and workers are constraining resources in the hypothetical shop. The organizational structure of the shop consists of divisions comprised of work centers that contain machines and workers. There are fewer workers than machines. Independent variables are interdivisional and intradivisional labor flexibility. Mean flow-time, flow-time variance and worker transfers between divisions and work centers are used as measures of shop performance. Labor flexibility is shown to have a major effect on shop performance. The effectiveness of interdivisional labor flexibility as a management variable is found to be concentrated in the region of high flexibility while intradivisional labor flexibility is most effective in the region of low flexibility.

In this paper, necessary conditions are obtained for optimal control problems containing equality constraints defined in terms of functions of the control and phase variables. The control system is assumed to be characterized by an ordinary differential equation, and more conventional constraints, including phase inequality constraints, are also assumed to be present. Because the first-mentioned equality constraint must be satisfied for all t (the independent variable of the differential equation) belonging to an arbitrary (prescribed) measurable set, this problem gives rise to infinite-dimensional equality constraints. To obtain the necessary conditions, which are in the form of a maximum principle, an implicit-function-type theorem in Banach spaces is derived.

This paper presents a technique for solving nonlinear programming problems with nonconvex feasible regions. The procedure expands the feasible region by replacing nonlinear equality constraints by appropriate inequality constraints. The expansion is used to solve two structural optimization problems using the sequential unconstrained-minimization technique of Fiacco and McCormick. The solutions are compared with solutions obtained by classical mathematical methods.

The current is running so swiftly in land-use affairs today that choosing a title for an essay on the problems in this turbulent field is perilous, a risk reflected in this essay's reference to the “police-power-eminent-domain deadlock.” Adherents of two trends that recently have attracted national attelltion might well dismiss an inquiry, so styled, as sterile, a throwback to misconceptions of the recent past. The first trend, fueled by the 1973 Council on Environmental Quality publication, The Taking Issue, urges that, short of actual appropriation, public measures that restrict private land use can never constitute a taking. The “deadlock” vanishes, of course, if constitutional notions of compensation as a constraint upon government regulation can be so easily defused. The second, a product of Bernard Siegan's provocative studies in Houston and his dalliance with University of Chicago economics, largely moots the issue by substituting the marketplace for public regulation as the source of land...

Five experiments were conducted in which subjects were asked to attribute attitudes to target persons on the basis of opinion statements written under high constraints, i.e., the target persons were instructed to prepare the statements but were given no choice concerning the position to be endorsed. In previous studies it had been observed that reader-subjects tended to attribute attitudes in line with the opinion statement even when the writer obviously had no choice. However, in these earlier studies the opinion endorsements were actually standardized statements prepared by the investigators and they may have contained subtle cues indicating attitude strength. In the present experiments the statements were those actually written by other subjects in response to no choice instructions. Even though the subjects as attributors were well aware of these instructions, and had complied to the same instructions as target persons, attitudes in line with expressed opinions were attributed. In the final experiment, constraints were strengthened even further by the provision of specific arguments that had to be included in the opinion statements. Here the “over attribution effect” finally fell below significance. With the exception of such extreme variants of constraint, the results provide further evidence that people tend to make dispositional attributions to “explain” behavior, underestimating the role of environmental constraints.

The Development Problem The labor-absorption issue has been a main actor in the development literature for at least 2 decades. The problem has recently been elevated in urgency. Sources of this increasing concern are not difficult to find. First, the conflict between growth and distributional goals has become increasingly apparent. Nowhere has this conflict attracted more attention than in the last 2 decades of Brazilian development. Second, the conventional dualistic models, and policy upon which they are based, treated labor absorption in modern, high-skill and high-wage sectors as a passive respondent to overall successful capital accumulation. From this perspective, the only constraint on rapid rates of labor absorption was the domestic savings effort. The performance of the late 1950s and 1960s dashed that optimism as high rates of aggregate growth and industrialization apparently failed to generate equivalently rapid rates of labor absorption.' Brazilian experience up to 1960 is representative of this disappointing performance, since manufacturing employment growth was only 2.6 percent per annum while output growth rates were in excess of 9 percent.2 Analysts have since turned their attention to policy-induced price distortions and/or technological biases in industrial development as a means of accounting for the disappointing labor-absorption performance.3

Clout, H. D. 1974. Agricultural plot consolidation in the Auvergne region of Central France. Norsk geografisk Tidsskr. 28, 181–194. Plot consolidation has made great progress in the Paris Basin and has accentuated the agricultural contrast between northern innovation and southern backwardness. The Auvergne contains a wide range of agrarian structures, with environmental conditions being most favourable for farming in the lowland Limagnes. Detailed examination of Puy-de-Dome departement shows that most of the Limagnes have been consolidated, but little has been done in the uplands, which require other forms of structural change, including enlargement and re-afforestation. Plot consolidation is not a revolutionizing process since it cannot change land ownership, which is the ultimate constraint on its success.

This note deals with the manner in which dynamic problems, involving probabilistic constraints, may be tackled using the ideas of Lagrange multipliers and efficient solutions. Both the infinite and finite time horizon are considered. Under very general conditions, Lagrange-multiplier and efficient-solution methods will readily produce, via the dynamic-programming formulations, classes of optimal solutions. However there may be gaps in the constraint levels thus generated. It is shown that, providing we admit mixed policies, these gaps can be filled in and that, furthermore, the dynamic programming calculations may, in some general circumstances, be carried out initially in terms of pure policies, and optimal mixed policies can be generated from these. The probabilistic constraints are treated in two ways, viz., by considering situations in which constraints are placed on the probabilities with which systems enter into specific states, and by considering situations in which minimum variances of performance are required subject to constraints on mean performance. Finally the mean/variance problem is viewed from the point of view of efficient solution theory. It is seen that some of the main variance-minimization theorems may be related to this more general theory, and that efficient solutions may also be obtained using dynamic-programming methods.

T HE argument that the world is running out of raw materials has recently taken on a great deal of additional credibility. Oil prices have risen almost four-fold and many other commodities from wheat and sugar through to copper have also shown spectacular increases in price. In fact, the extent and ubiquity of the price increases in primary commodities has been unprecedented. One could almost say that never have so many commodities risen so far and so quickly in such a short time. There are several reasons for what has been happening, yet the proposition that the world is about to run out of raw materials is not one of them. As always in commodities, the reasons for the sharp movement in prices are due to factors on both the demand and supply sides. Had the price increases been due to resource depletion one would have expected the main factor on the supply side to have been the sheer limitation on increasing production beyond existing levels of capacity. But a closer look at the situation in most commodity markets will quickly reveal that production has not in fact been held back by an ultimate capacity constraint. On the contrary, the problems have been ones of disruption and dislocations in supply so that production has in many cases fallen well below potential capacity. This is true for agricultural commodities such as wheat, sugar and coffee where weather conditions have played havoc with the annual harvest or crop. Many metals have been hit by an unusual number of production disruptions due to strikes, political problems, as in Chile, or technical breakdowns at processing plants. This has been further aggravated by the introduction of stricter anti-pollution legislation as well as by one or two factors which have either forced the complete closure of processing plant pending the construction of new plant and equipment, or forced existing plant to operate at well below design capacities. Thus in zinc, for instance, around twenty per cent. of the non-socialist world smelting capacity has been closed down over the last three years. Even in the case of oil, where those who support the resource depletion argument can probably make out their strongest case, the price increases have also been associated with a substantial cutback in production.

least 40 years for research to be translated into classroom teaching tech niques. That estimate has proved painfully true in the area of specific language disability. Eight generations of K-3 children have had to fight battles against misunderstanding and mistaken identity since Orton's pioneer work. Five years ago, determined to translate research into practice, the Wayne-Carroll School system began a search for an economical and effective way to bring appropriate instruction to the child with specific language disability. In two years of experimentation the staff recognized four con straints which had undoubtedly contributed to the slow pace with which re search was being translated into efficient, effective SLD programs easily replicated in the public schools. The four stumbling blocks encountered were: (1) with the tight budg ets available, how to serve the large numbers of children needing help; (2) how to see and serve the SLD child as a complex human being rather than as "a language problem"; (3) how to convince the child, his teachers, and his parents that he could succeed; (4) how to cope with unique learn ing styles. The sheer numbers needing help becomes a constraint to an effective program in most public schools because at the outset schools underestimate the number of children needing help. Inevitably an evergrowing waiting list brings frustration to children, parents, and professional staff. Authorities outside the classroom may put the ratio of SLD children at one in twenty or twenty-five, but teachers in the classroom will tell you the percentage is much higher. On the basis of its research the Wayne staff has concluded that between 15-20 percent of all children have language problems which make conventional teaching techniques ineffective. The differing learning styles of this 15-25 percent demand teaching techniques far different from

Growth and Environment: A Model of Optimal Control. — Agrowth-cum-environment model is analyzed assuming reproducible factors of production subject only to economic constraints, fund factors like exhaustible or energy resources subject to environmental and economic constraints, and environmental services subject to the constraint of the assimilative capacity of the environment. The formal set-up of the model is severely aggregated, but particular attention is given to the admissable economic specification of the model framework.

WHILE formal demonstration of the general theorem of second best' is, in substance, unassailable since, like other impossibility theorems,2 its negative corollaries rest securely on the posited absence of empirical limitations, it must be admitted that its forceful presentation several years ago disturbed us somewhat and carried just so much farther the process of disillusion with conventional welfare economics. Not that we had any right to be disturbed, for it is clear enough now that in talking of optimum conditions we were, in any case, saying precious little; no more, in fact, than (assuming the appropriate degree of differentiability in our functions) that a constrained maximum entails necessary conditions. This much being conceded, the second-best theorem does no more than point out that, if additional constraints are imposed, the necessary conditions for a maximum are in general more complex.3 The obvious corollary follows that, in order to identify a maximum position in these conditions, it is necessary to forsake the optimum conditions that are strictly relevant only to the simple case of a single and familiar constraint. It might seem proper then to say no more on the matter until a great deal more of information has been unearthed about the economic world we live in. But with welfare economics in the dumps now in consequence of several attacks in the last decade, those who have not yet abandoned hope will be prompted to scrutinize these theorems more closely if only with a view to setting limits to the gradual erosion of confidence in the subject. In regard to the second-best theory, for instance, we may admit that in general one can say nothing in the absence of universal optimization; further, that the vast and intricate knowledge required in order to derive quantitatively exact second-best solutions will be denied us in the foreseeable future. Yet we may still be able to indicate certain easily conceived conditions that permit us to say something useful; in particular we may be able to discover circumstances which enable us to derive guidance from the familiar optimum rules even though these rules are not universally met.

In the literature on the growth of firms, two factors on the supply side have received great emphasis. The first factor is economies of scale. Where economies of scale are present, growing firms reap greater profits and command the resources needed for further growth. In addition, growth is also induced for the profit-maximizing firm by the prospect of still higher profits. The second factor is the group of organization parameters constraining growth (Penrose 1959). These parameters are related to the history of the firm and in general cause a fast-growing firm in one period to slow down in the next. Evidently the actual growth of firms is partly explained by the balance of these two factors. More specifically, it may be hypothesized that the constraint by organization parameters is reflected by a negative correlation between the growth rates of firms in successive time periods. The negative correlation, however, is expected to be weaker in those industries where economies of scale are large. The objective of the present paper is to test empirically this hypothesis at the plant level, focusing on the intraplant basis of organization parameters and economies of scale. It turns out that the more important impact of economies of scale on growth of plants is indirect. Plants of different sizes have different input structures and are therefore affected in different ways by the secular changes in the relative prices of inputs and in technology. With this indirect factor taken into consideration, a positive relationship is found between the correlation of growth rates of plants in successive time periods and economies of scale. However, the implications of economies of scale on the growth behavior of plants were more than offset by the opposite impacts of organization parameters. As a consequence, rapidly growing plants in one period are compelled to slow down their growth

Geometric arguments are used, to discuss optimal control problems with higher-order state variable inequality constraints. Solutions with boundary arcs as well as with isolated boundary points are treated.

This paper reconsiders the proposition put forward by many economists that monopolies would produce less durable assets than would competitive firms. The key assumption made is that assets are desired for the services they provide. It is shown that, as all firms desire to minimize the cost of providing any given service, monopoly and competitive firms will select the same degree of durability. Although this result is proved for goods subject to exponential decay, the result can be generalized to an arbitrary decay function. A number of earlier writers reached mistaken conclusion basically because of their neglect of the initial demand for the good. Durability choice by a monopolist is unaffected by price or demand conditions so long as the firm is permitted to operate in the elastic portion of the demand curve. Price regulation will have no effect on the choice of durability unless an attempt is made to force the firm to operate in the inelastic portion of the demand curve. If this attempt is made, output will remain unchanged and costs will be increased so as to satisfy the unit cost mark-up constraint. In this case, the regulator should ensure that durability remains unaltered at the previous level.

Structured design systems are systems in which the equations representing the equality and inequality constraints are sparse and highly precedenc orderable. An algorithm has been developed for such systems which is guaranteed, under certain assumptions, to arrive in a finite number of steps at a feasible point (that is, one which satisfies all the constraints) or to identify a subset of the constraints for which no feasible point can be found. The algorithm can be applied to a system with only inequality constraints or to a system with both equality and inequality constraints. The algorithm uses an indirect approach. It hypothesizes that a subset of constraints has no feasible region and then attempts to verify this conjecture. If successful, the subset is identified as infeasible and obviously no feasible point exists. If unsuccessful, either a new hypothesis can be generated or the algorithm has indirectly found a feasible point. Limited computational experience with the algorithm indicates that the number of steps required to find a feasible point for a system of constraints has been of the same order of magnitude as the total number of constraints in the system. For linear constraints, the efficiency of the algorithm has been comparable to phase one of the Simplex algorithm of Linear Programming.

Summary 1. Unsatisfactory eating habits are the rule rather than the exception among an unselected group of children, but only 15 per cent of the group show sufficiently unsatisfactory behavior to be called “feeding problems.” 2. Good appetite and good table behavior are closely related variables and are found in homes in which strict disciplinary methods are combined with approval of the child. 3. The type of strictness found in the homes of children with good appetites seems to be a strictness about a few essentials of behavior but not a strictness which completely determines the child's activities. This freer type of strictness seems to be psychologically healthful. The children from such homes tend to be socially well adjusted. 4. The strictness found in the homes of children with good table behavior seems to stem from an attempt of the parents to force the child into complete conformity to adult standards. This excessive constraint on the child's behavior seems to render him incapable of free and spontaneous behavior and to hamper his social adjustment. 5. A wide acceptance of foods and lack of finicalness is most generally obtained by an abundance of affection and attention. There is no evidence that a coercive discipline in the home can make children nonfinical.

In a recent article in this journal, Morley reconsidered the problem of monetary stabilization in Brazil between 1963 and 1967.1 Using quarterly data of money, credit, output, and prices, instead of annual statistics as earlier writers had done, he demonstrated that Brazil did not suffer from continuous "stagflation"; on the contrary, the economy experienced short periods of rapid increases of money supply, expanding output, and inflation, interrupted by monetary constraint which in turn lowered production but not prices. Morley explained the persistent inflation during times of credit scarcity and stagnation by business firms marking up their prices in order to obtain sufficient working capital. He supported this thesis by an analysis of corporations' balance sheets showing that profits increased substantially between 1963 and 1967. Unfortunately, the ingenuity which Morley used to analyze his data to reveal the effects of an uneven application of stabilization policies is missing when it comes to explaining the causes of these fluctuations. He states that "the heart of the program was monetary constraint," and at another point: "The Brazilian experience also suggests that orthodox monetary policy may be self defeating." 2 1 shall provide some evidence to show that first, monetary policy played only a minor role in the Brazilian stabilization program; second, that Morley ignored the influence which the sudden influx of foreign exchange and agricultural development had upon the money supply and prices; and third, that the validity of Morley's profit-push hypothesis can be questioned in the light of recently published data of corporate earnings in Brazil. The action program clearly outlined the role monetary policy was to play and the anticipated results this policy would produce in the economy. Since the government's increased demand for financial resources had left the private sector starved for funds during the early sixties, the program envisaged controlling the money supply by reducing the federal govern

Although for most social workers accustomed to working with authority, there is little hesitation in embodying effectively this factor within the stream of social work practice, there are for other social workers not well acquainted with this concept, many moral dilemmas in an area heavily structured with authoritarian standards. The social worker is confronted by such issues as—how can one help a person who rejects the intrusion of others in his life, without diminishing the dignity of that individual? How can one avoid the autocratic qualities of direction and the threatening constraint over behaviour which can not only demean, but also rob a person of making an unfettered choice? Is it possible to aid constructively the development of attitudes which line up with what society demands, when, for example, the individual knows that his liberty or the receipt of welfare assistance, or the custody of members of his own family, is contingent on his strict conformity with the advice of the social worker? Is t...

The analysis seeks to determine the impact of lagged regulation on a profit-maximizing firm subject to a rate-of-return constraint. We are particularly interested in the effect of lag on the accomplishment of two regulatory goals: minimum-cost production, and an output greater than that of an unconstrained monopoly. The extend to which these goals are reached depends on whether the fair rate of return is equal to the cost of capital or somewhat higher. If the two are equal, lagged regulation accomplishes both goals; this contrasts sharply with continuous regulation, where the firm is indifferent among all methods of production or levels of output that let it break even in its operations. If the rate of return is above the cost of capital, it will not always pay for the firm to alter its resource allocation from the overcapitalized level indicated by Averch and Johnson. There will, however, be some length of the lag interval above which the firm will overcapitalize by successively smaller amounts, with attendant increases in output from the Averch-Johnson level.

SUMMARY Recent studies have stressed that a foreign exchange constraint can be limiting the rate of output growth in many developing countries. On the basis of a simple constraints model the role of tariffs and related import substitution in relieving a foreign exchange constraint are analyzed. It is first argued that the assumptions necessary for a foreign exchange constraint to be limiting output growth require that the optimal government intervention is through non-uniform exchange rate adjustment implied by trade controls and multiple exchange rates. But, whereas the optimum government intervention is through the establishment of a structure of optimum tariffs and subsidies, such a policy is not feasible in light of data availability and administrative capacity in developing countries. The costs and benefits of a non-optimal intervention through controls are then explored and standards of minimum acceptability of developing countries’ trade policies are established against which actual policy can be compared. It is concluded that trade controls can be used to improve growth performance but only if a number of rigid conditions are met.

Both tractors and milking machines were available to British farmers from the early 19OO's, but the mechanisation of field work and of dairy farming was not general until the 1950's. This paper discusses the technical difficulties of early forms of farm machinery, and the reorganisation of farm work which was required to use the machinery efficiently. Tractors were at first adopted for heavy work, thus easing the pressure on, and increasing the efficiency of, the horses. It was not until after the second world war that tractors and their implements became sufficiently reliable and versatile to supplant horses in all farm operations and to change an important constraint upon the structure of farms and the methods of working them.

The optimum tapering of Bernoulli—Euler beams, i.e. the shape for which a given total mass yields the highest possible value of the first fundamental frequency of harmonic transverse small oscillations, is determined. The question of the existence of a solution to the optimization problem is considered. It is shown that, irrespective of the relationship between the flexural rigidity and linear mass density of the cantilever beam, the necessary conditions for optimality lead to a contradiction. This result is in partial disagreement with that obtained by earlier investigators. By imposing additional constraints on the optimization variable, a numerical solution for the case of the cantilever beam is obtained, using the formulation of the maximum principle of Pontryagin.

The long-term air quality objectives in the San Francisco Bay Area strive to return the quality of air to 1940 conditions as a best condition but under no circumstances to permit the quality of air to deteriorate below 1970 conditions. Although some improvement in air quality is to be expected over the next decade because of stricter automobile pollution controls, it is expected that the pressure of a rapidly increasing population will tend to overwhelm these otherwise encouraging improvements. Using a simple homogeneous mixing model of the San Francisco air basin as an illustration, a maximum pollution-level constraint on each of several pollutants is derived using the air quality standards of the State of California. In view of the fact that pollution derived from transportation is considered to be the major source function, an analytic model is developed whereby state or federal decision makers can tradeoff various transportation options in order to meet the demand of an ever increasing commuting public while at the same time staying within a given pollution-level constraint. Although the approach presented is developed using derived data assuming a simple homogeneous mixing model and specifically addresses the transportation problem, the tradeoff approach is easily generalized to accepting data derived from more sophisticated models as they become available as well as extended to other sources of pollution suich as power plants and industrial systems.

Latin America has been sparsely populated since colonial times. The importation of slaves during the first half of the 19th century and European immigration during the second half have provided the manpower needed for the expansion of the Latin American colonial economies. At the end of the last century, industrialization in the form of import substitution began where sufficiently large domestic markets, brought about through increasing exports, permitted it. Consumer goods industries were created near population centers of sufficient size to provide a sizeable domestic market. After 1930, development became the driving force of economic growth in several Latin American countries. The extent to which import substitution could be accomplished depended on the size of the domestic market in each country. This is the reason that industrialization has made more headway in the three largest countries of the area. The small population size of many Latin American countries is now a constraint to their development. The enlargement of their domestic markets through the formation of free trade areas may spur development, but this cannot be achieved in the near future. For them, population growth is still important. Fertility is, however, already decreasing in Latin America and population growth is likely to diminish in the near future. In order to develop, most Latin American countries will have to integrate a larger proportion of their population into the markets, since they will not be able to continue to rely on population growth for the expansion of effective demand.

TO AN ECONOMIST the study of economic development is in large part an investigation into the mechanics of capital formation. At least in theory, the output options open to a developing economy are more restricted in the case where possibilities for obtaining foreign exchange via trade or aid are relatively limited. Society's menu of choices is even easier to enumerate if it is further assumed that labor is surplus in the sense that labor supply is a non-binding constraint on economic development now and for some time to come. These conditions are roughly descriptive of the historical situation confronting some large underdeveloped nations wishing to industrialize rapidly; the U.S.S.R. in the thirties is a classic example. In such situations the key to economic growth is the capacity of the domestic capital goods sector. Increasing that capacity by ploughing back a high proportion of investment goods for purposes of self-reproduction will permit high consumption levels eventually, but not just in the near future. The reverse is true if, by bolting down a substantial percentage of investment goods there, the consumer goods sector is presently expanded. These thoughts underlie a very interesting model of economic development first propounded by the Soviet engineering economist G. A. Fel'dman in 1928 [7] 2 We are indebted to Professor Domar [6] for pointing out the significance of this model and for relating it to current growth theory as well as to the Soviet industrialization debate of the twenties. The same model has been independently formulated by the Indian statistician P. C. Mahalanobis [9] who places somewhat greater emphasis on making it operational enough to serve as a rough guide of sorts for Indian long term planning.3 In its simplest form this model splits an economy into two departments, investment and consumption. Investment goods are general ex ante and can be used to increase the capacity of either sector. But ex post, capital is specific to the

A method is presented for the scheduling of a company's investments of its predictable, short-term, excess cash. The problem is structured in a way that leads to a fairly simple dynamic programming algorithm. The method is very flexible with regard to the type of investments considered; no structural properties of rates of return or availability are made except that they are predictable. The method allows the choice of holding to maturity or not and the choice can differ for different types of investments. A bank constraint, which fixes the average bank balance over the planning period, is added and the method of solution obtained.

This study is a follow-up to an earlier publication which looked at migrant female head porters' enrolment in, renewal and utilisation of the National Health Insurance Scheme in the Kumasi Metropolis. Head porterage in the large urban markets in Ghana comes with several health issues. Research has shown that migrant female head porters are exposed to several physical, social and psychological health risks in their daily encounters with clients. This research, therefore, aims at examining the health-seeking behaviours of migrant female head porters in the Kumasi metropolis using the dimensions of availability, accessibility, affordability, accommodation and acceptability. The researcher used the cross-sectional survey in the context of quantitative approaches. A total of 378 respondents were sampled from the following markets (Asafo, Adum shopping centres, Bantama and Kejetia) in which the migrant female head porters operate through convenient snowball sampling technique. Charts, percentages and tables were used in the data analysis. The study uncovered that the most (67%) preferred healthcare provider among the female head porters was over-the-counter chemical seller. Meanwhile, these service providers pose a serious health risk as they constitute a major source of self-medication. Further discoveries showed that affordability was the primary constraint to quality health-care as 76% of the respondents bemoaned charges at healthcare facilities. The study recommends a comprehensive policy interventions to enhance mass enrolment of female head porters unto the National Health Insurance Scheme to reduce the cost of healthcare among head porters. Finally, to protect the interest of the female head porters, they should form a well-structured and coordinated association to give them a united front to pursue their collective interest and protect them from the challenges they face including the difficulties they face in accessing healthcare.

During the last decade or so, substantial empirical work has been done on farmer response to price in the underdeveloped countries1. Most of the research effort, however, is lacking theoretical rigour and is heavily oriented towards the estimation of area (output) supply functions and the verification of the existence of economic incentives. The purpose of this study is to extend the research horizon by emphasizing and elaborating the role of certain constraints in determining the degree of farmer response to price which is one of the aspects of economic performance. We believe that the level of farmers' economic performance varies directly with their ability to exploit the opportunities within the horizon. It was main¬tained elsewhere that the basic reason for farmers' low level of economic performance lies in the fact that their ability to exploit given and well-understood opportunities is reduced by various constraints — physical (climate, water avail¬ability, etc.), technological (lack of more productive technical knowledge and knowhow, etc.) and institutional (the practice of subsistence farming) [12].

The empirical study revealed that among the various types of constraints (as perceived by the respondents) regarding the adoption of IPM technologies in the Pointed Gourd (Trichosan thes dioica Roxb.) production, the lack of knowledge of the respondents about the Economic Threshold Limit (ETL) concept ranked first closely followed by the lack of knowledge of the respondents regarding the bio-pesticides (under the category of knowledge and information constraints) in second position, the lack of knowledge of the respondents about the Integrated Pest Management (IPM) techniques ranked third position, closely followed by lack of training of the respondents on the proper use of pesticides in the fourth position. The result also showed that among six numbers of different categories of perceived constraints, knowledge and information constraints with a rank score of 2769 enjoyed first rank position, distantly followed by administrative and managerial constraints (with a rank score of 1586) in the second position, technological and communication constraints with a rank score of 1249 in the third position, socio-economic constraint (rank score of 828) in the fourth position. Keywords: Adoption of IPM techniques; Constraints; Categories of constraints DOI: 10.3329/jbau.v7i2.4722 J. Bangladesh Agril. Univ. 7(2): 219-227, 2009

This paper extends a simple economic model of the regulated firm to include a wider range of both management objectives and of regulatory constraint. The authors find that these generalizations in the assumptions are able to effect profound alterations in the conclusions. For example, if a firm is constrained to a fair return on invested capital, we find that the profit-maximizing firm would have an incentive to overcapitalize (the Averch-Johnson result), while the sales or output maximizing firm would have an incentive to undercapitalize. If any of several other methods of constraint are used, the authors find that there is no incentive to alter the relative amounts of labor and capital employed in the production process.

The purpose of this paper is to explain the relation between multiobjective planning of public investment programs and the use of budget constraints, because this important matter is normally not considered in governmental proposals of new planning methods. The multiobjective approach to planning includes: (1) identification of the several objectives of the public organization for which the plans are being made; (2) for each objective development of metrics of its benefits and costs; and (3) design of alternative programs that emphasize alternative combinations of objectives as a means of showing how governmental and private actions can contribute to objectives. In a formal sense a budget constraint is a limit on the total expenditure that can be made for a project or program; and if the constraint is binding, it affects the design of the project or program.

An analytic technique has been formulated which permits the management of an organization engaged in a number of research and engineering projects to allocate available technical manpower among and within projects. The technique has value as a device to determine in detail where men with specific skills may be best utilized and as a tool to gage the impact of proposed additional workload on available manpower resources and projects in progress. The technique makes use of the basic network analog to designate the sequence and interaction of the detailed activities making up each project. Judgments must be made by engineering management of the minimum essential manning and maximum productive manning required for each network activity to obtain the time-manpower function and its range of feasible values. The scheduled time for completion of each project must be stated as well as the total available manpower by skill, by time period. An integer solution is attained which is compatible with the available manpower constraint and which represents a practical economic optimum. The technique used is an iterative method suitable for computer computation.

A PRESIDENTIAL Address at a Society JLM. banquet is like a second dessert: one admires it politely, hesitates to receive it, and hopes that it will quickly pass by. The speaker may therefore be hopeful but not ambitious. He also suffers another constraint: he must remember that there are ladies present. It is not of course that, in these outspoken times, the presence of ladies need have the least effect on the purity of one's diction, the level of one's taste, or the temptation to use four-letter words, like “love.” It is rather that most of the ladies are sweethearts and wives, adorable and unprofessional, interested in Endocrinology in a very different way from us. The speaker must therefore be considerate of this qualified interest. There are also the ladies of our profession, the lovely and redoubtable few who wear our badge and speak our language.

external resource is a bridge to maintain the relationships among the economic entities. Foreign aid helps countries to come together in terms of humanitarian, commercial, strategic or political point of interests (Todaro, 1991, pp. 485-86). It has been the spotlight of huge number of research in recent years that how aid is contributing in the socio-economic development (Quibria, 1980). Bangladesh, a Least Developed Country (LDC), significantly depends on aid due to its resources constraint and also for establishing diplomatic relations with other countries as well as with the international agencies.