Strayer MAT 540 Week 9 and 10 Homework (2015) answers

MAT540 Homework

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 0.41MAT540 Homework

Week 9

Page 2 of 2

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, allterrain

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

A B C D Costs

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.

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Week 10 Homework

Chapter 6 1. Consider the following transportation problem:

From

To (cost)

1 2 3 Supply

A $ 5 $ 4 $3 130

B 2 3 5 70

C 4 8 7 100

Demand 80 110 60

Formulate this problem as a linear programming model and solve it by using the

computer.

2. Consider the following transportation problem:

From

To (cost)

1 2 3 Supply

A $ 5 $ 12 $ 2 130

B 2 9 5 70

C 4 24 7 100

Demand 80 110 60

Solve it by using the computer.

3. World Foods, Inc., imports food products such as meats, cheeses, and pastries to the United

States from warehouses at ports in Hamburg, Marseilles and Liverpool. Ships from these ports

deliver the products to Norfolk, New York and Savannah, where they are stored in company

warehouses before being shipped to distribution centers in Dallas, St. Louis and Chicago. The

products are then distributed to specialty foods stores and sold through catalogs. The shipping

costs ($/1,000 lb.) from the European ports to the U.S. cities and the available supplies (1000 lb.)

at the European ports are provided in the following table:

From

To (cost)

4. Norfolk 5. New York 6. Savannah Supply

1. Hamburg $420 $390 $610 55

2. Marseilles 510 590 470 78

3. Liverpool 450 360 480 37

The transportation costs ($/1,000 lb.) from each U.S. city of the three distribution centers and

the demands (1,000 lb.) at the distribution centers are as follows:

Warehouse Distribution CenterMAT540 Homework

Week 10

Page 2 of 2

7. Dallas 8. St. Louis 9. Chicago

4. Norfolk $ 75 $ 63 $ 81

5. New York 125 110 95

6. Savannah 68 82 95

Demand 60 45 50

Determine the optimal shipments between the European ports and the warehouses and the

distribution centers to minimize total transportation costs.

4. The Omega pharmaceutical firm has five salespersons, whom the firm wants to assign to five

sales regions. Given their various previous contacts, the salespersons are able to cover the

regions in different amounts of time. The amount of time (days) required by each

salesperson to cover each city is shown in the following table:

Region (days)

Salesperson

A B C D E

1 17 10 15 16 20

2 12 9 16 9 14

3 11 16 14 15 12

4 14 10 10 18 17

5 13 12 9 15 11

Which salesperson should be assigned to each region to minimize total time? Identify

the optimal assignments and compute total minimum time.