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.
1.
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
1.
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.
1.
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.
Use the following coupon code :
ACHIEVER30
