10 8 15 10 D 5 2 0 7 x E 6 10 x 9 11 Here minimum no. of horizontal and vertical straight lines to cover all the zeros = 5 = Order of the matrix So the solution is optimal. . Optimal Assignment Batsman Batting Position A VII Average runs scored 50 V10 B III 42 VI 60 D v 20 E IV 60 Total 232 Expected maximum total runs = 232 Illustration 3 Average time taken by an operator on a specific machine is tabulated below. The management is considering replacing one of the old machines by a new one and the estimated time for operation by each operator on the new machine is also indicated, Operator Machines M M M M . New M, 4 01 2 3 2 1 1 5 6 02 4 4 6 3 2 5 1 1 03 6 10 8 4 7 6 1 04 8 7 6 5 3 9 4 05 7 3 4 5 4 3 12 06 5 5 6 7 8 1 6 (a) Find out an allocation of operators to the old machines to achieve a minimum operation time. (b) Reset the problem with the new machine and find out the allocation of the operators to each machine and comment on whether it is advantageous to replace an old machine to achieve a reduction in operating time only. (c) How will the operators be reallocated to the machines after replacement