Assignment problem

1. (20 marks) A machine shop has six jobs waiting to be done. There are six machines available to do these jobs, and the shop will assign each job to a specific machine. The machines differ in their capabilities, so the times to do each job are different. The following table gives the number of minutes required to do each job, depending on the machine to which it is assigned. Machine Job 1 2 3 4 5 6 45 42 48 41 47 51 2 38 34 39 35 36 40 3 56 61 65 59 60 62 4 41 42 39 40 48 43 J 32 28 29 39 36 37 6 42 38 49 43 39 45 (a) The shop wishes to minimize the total number of minutes used to do these jobs. Use LINGO or the Excel Solver to determine the optimal solution. (b) State this solution so that anyone working in the shop would be able to under- stand it