Case 1:
Diamond Jeweler's is trying to determine how to advertise in order to maximize their exposure. Their weekly advertising budget is $10,000. They are considering three possible media: tv, newspaper, and radio. Information regarding cost and exposure is given in the table below:
|
Medium
|
audience reached per ad
|
cost per ad ($)
|
maximum ads per week
|
|
TV
|
7,000
|
800
|
10
|
|
Newspaper
|
8,500
|
1000
|
7
|
|
Radio
|
3,000
|
400
|
20
|
Case 2:
A manufacturer of microcomputers produces four models: Portable, Student, Office, and Network. The profit per unit on each of these four models is $500, $350, $700, and $1000, respectively. The models require the labor and materials per unit shown below.
|
|
Portable
|
Student
|
Office
|
Network
|
Total
|
|
Labor (hrs/week)
|
5
|
5
|
6
|
8
|
4000
|
|
Chassis (unit/week)
|
1
|
1
|
1
|
1
|
400
|
|
Disk Drive (unit/week)
|
2
|
1
|
2
|
1
|
300
|
|
Hard Disk (unit/week)
|
0
|
0
|
0
|
1
|
20
|
|
Memory Chip (unit/week)
|
16
|
8
|
32
|
64
|
22,000
|
|
Circuit Bds. (unit/week)
|
1
|
1
|
2
|
4
|
10,000
|
Formulate this product mix problem using linear programming.
Case 3:
First Securities, Inc., an investment firm, has $380,000 on account. The chief investment officer would like to reinvest the $380,000 in a portfolio that would maximize return on investment while at the same time maintaining a relatively conservative mix of stocks and bonds. The following table shows the investment opportunities and rates of return.
|
Investment Opportunity
|
Rate of Return
|
|
Municipal Bonds
|
0.095
|
|
High Tech Stock
|
0.146
|
|
Blue Chip Stock
|
0.075
|
|
Federal Bonds
|
0.070
|
The Board of Directors has mandated that at least 60 percent of the investment consist of a combination of municipal and federal bonds, 25 percent Blue Chip Stock, and no more than 15 percent High Tech Stock. Formulate this portfolio selection problem using linear programming.