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Compared to the traditional monostatic MIMO radar which uses uniform linear arrays (ULAs) for transmitting and receiving signals, sparse linear arrays (SLAs) monostatic MIMO radars can achieve greater Degrees Of Freedom (DOF) and a higher resolution. The optimal placement of sensors in both transmit and receive arrays to attain the maximum DOF is, however, a basic problem in the collocated monostatic MIMO radar. Optimum solution of such a problem is restricted to an exhaustive computer search. Some popular arrays such as nested and coprime arrays have been previously proposed as alternative solutions that can achieve a good DOF, but they do not necessarily lead to the maximum one. In this paper at first, we formulate the optimal placement of sensors in the collocated monostatic MIMO radar to improve the sum coarray as well as the difference coarray of the sum coarray. After that, we present a mathematical framework to achieve the optimal solution for both problems. Finally, we demonstrate that the proposed method yields the optimal MR-MIMO array while demanding much less computational complexity as compared with the computer search. [ABSTRACT FROM AUTHOR]