Problem 1

Four jobs are assigned to four machines. The cost to perform a job on each machine is shown.

1.1. Determine the solution that assigns jobs to machines at minimum total costs. You need to solve this problem as a linear programming problem.

1.2 Assume machine 2 and machine 3 can perform two jobs each, but don't have to. Machine 1 and 4 can perform one job if assigned. So, not all the machines must be used! All the jobs need to be performed. Write the constraints. Do not re-solve.

1.3 Assume again, that machine 2 and 3 can perform up to two jobs. However, exactly three jobs (out of the four jobs listed) must be performed. Which jobs should be chosen to minimize the total cost? To answer this question you can solve the problem multiple times. However, the challenge is to solve it once and have an answer. This requires one new constraint added to the model of part '1.2' [This constraint does not belong to the structure of the assignment model, but will force the number of projects performed be three. Also note that not all the jobs will be completed; This needs to be expressed by the model].

	Job1	Job2	Job3	Job4
Machine1	2300	2800	1850	4000
Machine2	2850	2980	3320	3450
Machine3	2500	2900	1900	3200
Machine4	3000	2950	2875	3350