Please help me out with these three problems. Please note that these problems need to be completed manually.
7-14 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 production-mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the corner point graphical approach.
7-15 Electrocomp's management realizes that it forgot to include two critical constraints (see Problem 7-14). In particular, management decides 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.
(a) If Electrocomp decides that at least 20 air conditioners should be produced, but no more than 80 fans should be produced, what would be the optimal
solution? How much slack is there for each of the four constraints?
(b) If Electrocomp decides that at least 30 air conditioners should be produced, but no more than 50 fans should be produced, what would be
the optimal solution? How much slack is there for each of the four constraints at the optimal solution?
7-18 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 an 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?
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The solution provides detailed explanation how to solve linear programming problems by graph method in an attached Word file.
Quantitative Methods Exercises
The Southern Sporting Goods Company makes basketballs and footballs. Each product is produced from two resources - rubber and leather. The resource requirements for each product and the total resources available are as follows.
Resource Requirements per unit
Product Rubber (lb) Leather ( ft2 )
Basketball 3 4
Football 2 5
Total resources available 500 lb 800 ft2
Each basketball produced results in a profit of $12, and each football earns $16 in profit.
a. Formulate a linear programming model to determine the number of basketballs and footballs to produce in order to maximize profits.
b. Transform this model into standard form.
Solve the model formulated in problem #5 for the Southern Goods Company graphically.
a. Identify the amount of unused resources (i.e., slack) at each of the graphical extreme points.
b. What would be the effect on the optimal solution if the profit for a basketball changed from $12 to $13? What would be the effect if the profit for a football changed from $16 to $15?
c. What would be the effect on the optimal solution if 500 additional pounds of rubber could be obtained? What would be the effect if 500 additional square feet of leather could be obtained?