Saint GBA334 module 5 homework

Problem 7-14

Graphical Solution:The Electorcomp 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 or $25. Each fan assembled may be sold for a $10 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach.

Problem 7-17

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 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. How many benches and tables should Outdoor Furniture produce to obtain the largest possible profit? Use the graphical LP approach.

7-20 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 following table provides a summary of the return and risk:

Stock	Estimated Return	Risk Index
Petrochemical	12%	9
Utility	6%	4

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. How much should be invested in each stock? What is the average risk for this investment? What is the estimated return for this investment?

Let X₁ = the number of dollars invested in petrochemical stocks

X₂ = the number of dollars invested in utility stocks

7-24 The stock brokerage firm of Blank, Leibowitz, and Weinberger has analyzed and recommended two stocks to an investors’ club of college professors. The professors were interested in factors such as short term growth, intermediate growth, and dividend rates. These data on each stock are as follows:

	Stock
Factor	Louisiana Gas and Power	Trimex Insulation Company
Short term growth potential, per dollar invested	.36	.24
Intermediate growth potential (over next three years), per dollar invested	1.67	1.5
Dividend rate potential	4%	8%

Each member of the club has an investment goal of (1) an appreciation of no less than $720 in the short term, (2) an appreciation of at least $5,000 in the next three years, and (3) a dividend income of at least $200 per year. What is the smallest investment that a professor can make to meet these three goals?