Reference no: EM132253005

Assignment -

Part A - Chapter 2 Exercises.

For all problems use Excel Solver. Graphical solution not required.

Problem 1 - Solve the following LP problem by using the graphical procedure and by using Excel:

Maximize profit = 2X + Y

subject to the constraints

3X + 6Y ≤ 32

7X + Y ≤ 20

3X - Y ≥ 3

X, Y ≥ 0

Problem 2 - Solve the following LP problem by using the graphical procedure and by using Excel:

Minimize cost = 4X + 7Y

subject to constraints

2X + 3Y ≥ 60

4X + 2Y ≥ 80

X ≤ 24

X, Y ≥ 0

Problem 3 - Solve the following LP problem by using the graphical procedure and by using Excel:

Minimize cost 4X + 7Y

subject to the constraints

3X + 6Y ≥ 100

10X + 2Y ≥ 160

2Y ≥ 40

2X ≤ 75

X, Y ≥ 0

Problem 4 - A small motor manufacturer makes two types of motor, models A and B. The assembly process for each is similar in that both require a certain amount of wiring, drilling, and assembly. Each model A takes 3 hours of wiring, 2 hours of drilling, and 1.5 hours of assembly. Each model B must go through 2 hours of wiring, 1 hour of drilling, and 0.5 hours of assembly. During the next production period, 240 hours of wiring time, 210 hours of drilling time, and 120 hours of assembly time are available. Each model A sold yields a profit of $22. Each model B can be sold for a $15 profit. Assuming that all motors that are assembled can be sold, find the best combination of motors to yield the highest profit.

Part B - Chapter 3 Exercises

Problem 1 - A contestant on the hit reality television show Top Bartender was asked to mix a variety of drinks, each consisting of 4 fluid ounces. No other ingredients were permitted. She was given the following quantities of liquor:

The contestant is considering making the following four drinks:

• The New Yorker: 25% each of bourbon, brandy, vodka, and sweet vermouth.
• The Garaboldi: 25% each of brandy and dry vermouth; 50% sweet vermouth.
• The Kentuckian: 100% bourbon.
• The Russian: 75% vodka and 25% dry vermouth.

The contestant's objective is to make the largest number of drinks with the available liquor. What is the combination of drinks to meet her objective?

Problem 2 - A gear manufacturer is planning next week's production run for four types of gears. If necessary, it is possible to outsource any type of gear from another gear company located nearby. The following table and the table at the bottom of this page show next week's demand, revenue per unit, outsource cost per unit, time (in hours) required per unit in each production process, and the availability and costs of these processes. The nearby company can supply a maximum of 300 units of each type of gear next week. What should be the production and/or outsource plan for the next week to maximize profit?

Problem 3 - A political candidate is planning his media budget for an upcoming election. He has $90,500 to spend. His political consultants have provided him with the following estimates of additional votes as a result of the advertising effort:

• For every small sign placed by the roadside, he will garner 10 additional votes.
• For every large sign placed by the roadside, he will garner 30 additional votes.
• For every thousand bumper stickers placed on cars, he will garner 10 additional votes.
• For every hundred personal mailings to registered voters, he will garner 40 additional votes, and
• For every radio ad heard daily in the last month before the election, he will garner 485 additional votes.

The costs for each of these advertising devices, along with the practical minimum and maximum that should be planned for each, are shown on the following table. How should the candidate plan to spend his campaign money?

Formulate this portfolio selection problem by using LP and solve it by using Excel.

Problem 4 - An investor wishes to invest some or all of his $12.5 million in a diversified portfolio through a commercial lender. The types of investments, the expected interest per year, and the maximum allowed percentage investment he will consider are shown on the following table. He wants at least 35% of his investments to be in nonmortgage instruments and no more than 60% to be in high-yield (and high-risk) instruments (i.e., expected interest > 8%). How should his investment be diversified to make the most interest income?

Note - Solutions should be in Excel format!!!