A workshop has 5 jobs to perform today. Each job must be done by exactly one machine, but a machine can do more than one job. For each machine, there is a setup cost for the regular workday. Once this cost is paid, you can use the machine for up to 8 hours; if you do not pay the setup cost, you cannot use the machine today. If you set up a machine for the regular workday, you may also elect to set up the machine for overtime, in which case there is an additional cost and you may use the machine for up to 2 more hours. On the other hand, if you do not set up a machine for the regular workday, it cannot be used for overtime. The costs are as follows:
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Setup Cost Overtime Setup Cost
Machine 1
$ 600 $ 190
Machine 2
$ 700 $ 200
Machine 3
$ 550 $ 275
Machine 4
$ 675 $ 150
Machine 5
$ 585 $ 195
Thus, if you pay $600, you can use machine 1 for up to 8 hours, and if you pay $600 + $190 = $790, you may use machine 1 for up to 8 + 2 = 10 hours. The number of hours each job takes on each machine is as follows:
Job 1 Job 2 Job 3 Job 4 Job 5
Machine 1 3.0 4.0 5.5 2.5 3.1
Machine 2 3.8 4.9 6.4 2.9 2.7
Machine 3 3.6 4.8 5.5 3.8 2.8
Machine 4 2.9 5.3 5.6 2.9 1.9
Machine 5 3.1 6.0 5.1 2.6 2.5
a. Define the decision variables
b. Develop the objective function
c. Write the constraints