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Linear Programming Modeling Applications: With Computer Analyses in Excel

PROBLEMS 1. 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 Municipal Bonds High Tech Stock Blue Chip Stock Federal Bonds

Rate of Return 0.095 0.146 0.075 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 and find solution with Excel.

2. Cedar Point amusement park management is preparing the park's annual promotional plan for the coming season. Several advertising alternatives exist: newspaper, television, radio, and displays at recreational shows. The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium. Given an advertising budget of $250,000, how many placements should be made in each medium to maximize total audience exposure? Formulate this as a linear programming problem and find optimal solution with Excel software. Type

Cost

Newspaper Television 2200 Radio Shows

1500

Maximum number

Exposure (1000s)

100 50

750 150

80 120

50 3

45 10

3. 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. Labor (hrs/week) Chassis (unit/week) Disk Drive (unit/week) Hard Disk (unit/week) Memory Chip (unit/week) Circuit Bds. (unit/week)

Portable 5 1 2 0 16 1

Student 5 1 1 0 8 1

211

Office 6 1 2 0 32 2

Network 8 1 1 1 64 4

Total 4000 400 300 20 22000 10000

Linear Programming Modeling Applications: With Computer Analyses in Excel

Formulate this product mix problem using linear programming and solve with Excel software.

4. Green Grass, Inc. just ran out of stock and suddenly has two emergency orders for grass seed blends: one is for 1500 pounds of normal, the other for 2300 pounds of special. At most, each pound of normal should contain 60 percent annual seed, while each pound of special should contain at least 70 percent perennial seed. Green Grass has two input mixtures, A and B. Mixture A contains 80 percent perennial and 15 percent annual seed. Mixture B contains 70 percent annual and 25 percent perennial seed. Mixture A costs 90 cents per pound and mixture B costs 50 cents per pound. Set up the constraints and the objective function to solve this blending problem with Excel software.

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Linear Programming Modeling Applications: With Computer Analyses in Excel

5.

Friendly Manufacturing has three factories (1, 2, and 3) and three warehouses (A, B, and C). The table below shows the shipping costs between each factory (in dollars) and warehouse, the factory manufacturing capabilities (in 1000s) and the warehouse capacities (in 1000s). Write the objective function and the constraint inequalities. Solve this problem with Excel.

From Factory 1 Factory 2 Factory 3 Capacity

A 6 8 11 7

To B 5 10 14 12

Production Capability 6 8 10

C 3 8 18 5

6. Ivana Myrocle wishes to invest her inheritance of $250,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways  CDs, which pay a guaranteed 8 percent; stocks, which have an expected return of 12 percent; and a money market mutual fund, which is expected to return 10 percent. She has decided that the total $250,000 will be invested, but any part (or all) of it may be put in any of the three alternatives. Thus, she may have some money invested in all three alternatives. She has also decided to invest at least 20 percent of this in stocks and at least 20 percent of this in CDs. Formulate this as a linear programming problem and carefully define all the decision variables then solve to find solution with Excel.

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