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MAT540 Homework Week 9

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MAT540

Week 9 Homework

Chapter 5

1. The Livewright Medical Supplies Company has a total of 12 salespeople it wants to assign to

three regions – the South, the East, and the Midwest. A salesperson in the South earns $600 in

profit per month of the company, a salesperson in the East earns $540, and a salesperson in the

Midwest earns $375. The southern region can have a maximum assignment of 5 salespeople.

The company has a total of $750 per day available for expenses for all 12 salespeople. A

salesperson in the South has average expenses of $80 per day, a salesperson in the East has

average expenses of $70 per day, and a salesperson in the Midwest has average daily expenses

of $50. The company wants to determine the number of salespeople to assign to each region to

maximize profit.

a. Formulate an integer programming model for this problem

b. Solve this model by using the computer.

2. Solve the following mixed integer linear programming model by using the computer:

Maximize Z = 5 x1 + 6 x2 + 4 x3

Subject to 5 x1 + 3 x2 + 6 x3 ≤ 20 x1 + 3 x2 ≤ 12 x1, x3 ≥ 0 x2 ≥ 0 and integer

3. 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.

Project Expense ($1,000s)

Management Scientists required

Estimated Profit (1,000,000s)

1 $ 60 7 $0.36

2 110 9 0.82

3 53 8 0.29

4 47 4 0.16

5 92 7 0.56

6 85 6 0.61

7 73 8 0.48

8 65 5 0.41

MAT540 Homework Week 9

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Formulate the integer programming model for this problem and solve it using the computer.

4. During the war with Iraq in 1991, the Terraco Motor Company produced a lightweight, all-

terrain vehicle code-named “J99-Terra” for the military. The company is now planning to sell

the Terra to the public. It has five plants that manufacture the vehicle and four regional

distribution centers. The company is unsure of public demand for the Terra, so it is considering

reducing its fixed operating costs by closing one or more plants, even though it would incur an

increase in transportation costs. The relevant costs for the problem are provided in the

following table. The transportation costs are per thousand vehicles shipped; for example, the

cost of shipping 1,000 vehicles from plant 1 to warehouse C is $32,000.

From Plant

Transportation Costs ($1000s) to Warehouse Annual Production

Capacity

Annual Fixed Operating

Costs A B C D

1 $56 $21 $32 $65 12,000 $2,100,000

2 18 46 7 35 18,000 850,000

3 12 71 41 52 14,000 1,800,000

4 30 24 61 28 10,000 1,100,000

5 45 50 26 31 16,000 900,000

Annual Demand

6,000 14,000 8,000 10,000

Formulate and solve an integer programming model for this problem to assist the company in

determining which plants should remain open and which should be closed and the number of

vehicles that should be shipped from each plan to each warehouse to minimize total cost.