Linear Problems


1. 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. 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.



2. The dean of the Western College of Business must plan the school’s course offerings for the fall semester. Student demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in total. Each undergraduate course taught costs the college and average of $2,500 in faculty wages, and each graduate course costs $3,000. How many undergraduate and graduate courses should be taught in the fall so that total faculty salaries are kept to a minimum?



3. Consider the following LP problem:

Maximize profit = 5X + 6Y

Subject to 2X + Y < 120

2X + 3Y 0

A.What is the optimal solution to this problem? Solve it Graphically.

B.Of a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution?

C.Instead of an increase in the profit coefficient X to $8, suppose that profit was overestimated and should only have been $3. Does this change the optimal solution?



4. Consider the LP formulation given in Problem 7-31. If the second constraint is changed from 2X + 3Y < 240 to 2X + 4Y < 240, what effect will this have on the optimal solution?



5. Eddie Kelly is running for reelection as mayor of a small town in Alabama. XXXXX XXXXX, XXXXX’s campaign manager during this election, is planning the marketing campaigen, and there is some stiff competition. Martinez has selected four ways to advertise: television ads, radio ads, billboards, and newspaper ads. The costs of these, the audience reached by each type of ad, and the maximum number of each is shown in the following table:

TYPE OF AD COST PER AD AUDIENCE REACHED/AD MAXIMUM NUMBER

T.V. $800 30,000 10

Radio $400 22,000 10

Billboards $500 24,000 10

Newspapers $100 8,000 10

In addition, Martinez has decided that there should be at least six ads on TV or radio or some combination of those two. The amount spent on billboards and newspapers together must not exceed amount spent on TV ads. While fundraising is still continuing, the monthly budget for advertising has been set at $15,000. How many ads of each type should be placed to maximize the total number of people reached?



Please explain and show your work. I really appreciate your assistance. In problem 3 and 4 the underline that goes with the did not copy over from my word document that I had type the problems on before pasting it here
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