# MATHEMATICS

Part 1 of 5

The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit.

Now, Electrocomp’s management also realizes that there should be a minimum number of air conditioners produced in order to fulfill a contract. Also, due to an oversupply of fans in the preceding period, a limit should be placed on the total number of fans produced.

1. If Electrocomp decides that at least 20 air conditioners should be produced but no more than 80 fans should be produced, the optimal production mix of air conditioners and fans is _____________ (The first number is for air conditioners and the second is for fans

a. (50, 30)

b. (20, 80)

c. (40, 60)

d. (26.67, 80)

2. In the optimal solution for the above question (Question 1), the slack for the four constraints – Total hours of wiring, Total hours of drilling, Number of air conditioners, Number of fans are _________, respectively. (Hint: A negative number shows that the constraint is binding downward, i.e. it sets a lower rather than an upper limit. Take the negative sign out when interpreting the results.)

a. 0, 0, 20, 20

b. 0, 0, 10, 20

c. 0, 0, 20, 10

d. 10, 10, 10, 10

3. If Electrocomp decides that at least 30 air conditioners should be produced but no more than 50 fans should be produced, the optimal production of air conditioners is 45 and the optimal productions of fans is 50 (Only enter an integer and include no units.)

4. In the optimal solution for the above question (Question 3), the slack for the four constraints – Total hours of wiring, Total hours of drilling, Number of air conditioners, Number of fans are __________, respectively. (Hint: A negative number shows that the constraint is binding downward, i.e. it sets a lower rather than an upper limit. You may take the negative sign out when interpreting the results)

a. 0, 0, 15, 10

b. 5, 0, 15, 0

c. 0, 5, 15, 0

d. 0, 0, 10, 15

Part 2 of 5

The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm also has a stock of 3,500 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 4 labor hours and 10 feet of redwood; each picnic table takes 6 labor hours and 35 feet of redwood. Completed benches will yield a profit of $9 each, and tables will result in a profit of $20 each.

5. The optimal production of benches is262 and the optimal production of tables is 25.(Please only include the integer and no units. Hint: Because of the resource constraints, you may not be able to produce 4 tables even if the solution is 3.8; you may have to just produce 3 tables)

Part 3 of 5

A winner of the Texas Lotto has decided to invest $50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1–10 (with 10 being the most risky) is assigned to each of the two stocks. The total risk of the portfolio is found by multiplying the risk of each stock by the dollars invested in that stock. The attached table provides a summary of the return and risk. The investor would like to maximize the return on the investment, but the average risk index of the investment should not be higher than 6.

Stock

Estimated Return

Risk Index

Petrochemical

12%

9

Utility

6%

4