Improved Matrix Showing Optimal Solution (ii) New M 2 Machines M M M X O 5 2 X 1 M 6 Operator M 01 02 O 03 2 7 X 1 4 7 4 1 1 6 5 O 1 04 2 X 0 6 & 2 05 2 0 2 X 3 2 11 v11 3 1 4 7 06 Dummy 2 O 5 3 X 1 1 3 3 Table Showing Multiple Optimum Allocations Solution (1) Operators M/C Time (Hrs.) Operators 01 M M 2 01 02 M M 3 02 03 New 1 03 04 M 3 04 05 M, 3 05 06 M 1 06 Dummy M 0 Dummy Total 13* Total Solution (1) Solution (1) M/C Time (Hrs.) Operators M/C Time (Hrs.) M, 5 01 M 1 . 1 02 M 4 New 6 03 New 1 M. 0 04 M 3 . 3 05 M 3 M 7 06 M 1 M 3 Dummy M 0 13* Total 13* Minimum Operation Time From above it can be said that replaement of an old machine with the new one will result in a reduction in Total Operating Time by 17-13 = 4 Hours. So replacement decision is advantageous. As per solutions (i) & () above, Machine M, should be replaed by a New Machine and as per Solution (). M, should be replaced by a New one. . Illustration 4. Six salesmen are to be allocated to six sales regions so that the cost of allocation of the job will be minimum. Each salesman is capable of doing the job at different cost in each region. The cost matrix is given below: Region III IV V 1 15 II 35 VI 45 0 25 10 A B 45 20 40 25 25 D Salesmen 5 60 20 70 25 10 35 65 10 5 40 E 30 40 15 20 25 10 25 60 40 50 50 15 (Figures are in Rupees) F 10 30 (a) Find thiucation to give minimum cost. What is the minimum cost? (b) Now suppose the above table gives earning of each salesman at each region. How can you find an allocation so that the earning will be maximum? Determine the solution with optimum earning. (c) There are restrictions for commercial reasons that A cannot be posted to region V and E cannot be posted to region II. Write down the cost matrix suitably after imposing the restrictions