Strayer MAt540 week 9 assignment

MAT540
Week
9 Homework
Chapter 5
6.
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.

10.
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

14.
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

Formulate the
integer programming model for this problem and solve it using the computer.
20.
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.

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