Problem 13: Electrocomp\'s management realizes that it forgot to include two cri
ID: 427360 • Letter: P
Question
Problem 13: Electrocomp's management realizes that it forgot to include two critical contraints. (see Problem 14). In particular, management decides that there should be a minimum number of air conditioners produced Beta 5. The firm employs five technicians, working 160 hours each per month, on its assembly line. Management insists that full employment (i.e., all 160 hours of time) be maintained for each worker during next month's operations. It requires 20 labor hours to assemble each Beta 5 model. MSA wants to see at least 10 Alpha 4s and at least 15 Beta 5s produced during the production period. Alpha 4s generate $1,200 profit per unit, and Beta 5s yield $1,800 each. Determine the most profitable number of each model of minicomputer to produce during the coming month.
Problem 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 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. (this problem only here for resource in order to solve problem 13)
Explanation / Answer
ISM 6407 Fall 2009LINEAR PROGRAMMING FORMULATION PROBLEMS AND SOLUTIONS7-14 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 anddrilling. 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 ofwiring time are available and up to 140 hours of drilling time maybe used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate and solvethis 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.Let X1 = the number of air conditioners scheduled to be producedX2 = the number of fans scheduled to be producedMaximize 25X1+ 15X2(maximize profit)Subject to: 3X1+ 2X2? 240 (wiring capacity constraint)2X1+ X2? 140 (drilling capacity constraint)X1, X2? 0 (non-negativity constraints)Optimal Solution: X1 = 40 X2 = 60 Profit = $1,9007-15 Electrocomp’s management realizes that it forgot to include two critical constraints (see Problem7-14). In particular, management decides that to ensure an adequate supply of air conditioners fora contract, at least 20 air conditioners should be manufactured. Because Electrocomp incurred anoversupply of fans in the preceding period, management also insists that no more than 80 fans beproduced during this production period. Resolve this product mix problem to find the new optimal solution.Let X1 = the number of air conditioners scheduled to be producedX2 = the number of fans scheduled to be producedMaximize 25X1+ 15X2(maximize profit)Subject to: 3X1+ 2X2? 240 (wiring capacity constraint)2X1+ X2? 140 (drilling capacity constraint)X1? 20 (a/c contract constraint)X2? 80 (maximum # of fans constraint)X1, X2? 0 (non-negativity constraints)Optimal Solution: X1 = 40 X2 = 60 Profit = $1,900
ISM 6407 Fall 20097-16 A candidate for mayor in a small town has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: radio and television. Each radio ad costs $200 and reaches an estimated 3,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of radio ads must be at least as great as the number of television ads. How many ads of each type should be used? How many people will this reach?Let X1 = the number of radio ads purchasedX2 = the number of television ads purchasedMaximize 3,000X1+ 7,000X2(maximize exposure)Subject to: 200X1+ 500X2? 40,000 (budget constraint)X1? 10 (at least 10 radio ads purchased)X2? 10 (at least 10 television ads purchased)X1? X2(# of radio ads ? # of television ads)X1, X2? 0 (non-negativity constraints)For solution purposes, the fourth constraint would be rewritten as:X1? X2? 0Optimal Solution: X1 = 175 X2 = 10 Exposure = 595,000 people7-17 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 a supplyof 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 3500 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.Le