Question 1: Integer Programming (50 Points)

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:

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

e. Define the decision variables. (4 Points)

f. Develop the objective function. (4 Points)

g. Write the constraints. (9 Points)

h. Solve the problem in Excel. (18 Points: Decision variables section: 3 point,
O.F. Section: 3 points, Constraints section: 8 points, Solver: 4 points )

Question 2: Integer Programming (50 Points)

The Texas Consolidated Electronics Company is contemplating a research and development program encompassing eight research projects. The company is constrained from embarking on all projects by the number of available management scientists (40) and the budget available for R&D projects ($300,000). Further, if project 2 is selected, project 5 must also be selected (but not vice versa). Following are the resource requirements and the estimated profit for each project:

i. Define the decision variables. (6 Points)

j. Develop the objective function. (6 Points)

k. Write the constraints. (15 Points)

l. Solve the problem in Excel. (23 Points: Decision variables section: 4
points, O.F. Section: 4 points, Constraints section: 10 points, Solver: 5 points)