LP Formulation Problems & Solutions

LP Formulation Problems & Solutions - ISM 6407 Fall...

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ISM 6407 Fall 2009 LINEAR PROGRAMMING FORMULATION PROBLEMS AND SOLUTIONS 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 maybe 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. Let X 1 = the number of air conditioners scheduled to be produced X 2 = the number of fans scheduled to be produced Maximize 25X 1 + 15X 2 (maximize profit) Subject to: 3X 1 + 2X 2 240 (wiring capacity constraint) 2X 1 + X 2 140 (drilling capacity constraint) X 1 , X 2 0 (non-negativity constraints) Optimal Solution: X 1 = 40 X 2 = 60 Profit = $1,900 7-15 Electrocomp’s management realizes that it forgot to include two critical constraints (see Problem 7-14). In particular, management decides that to ensure an adequate supply of air conditioners for a contract, at least 20 air conditioners should be manufactured. Because Electrocomp incurred an oversupply of fans in the preceding period, management also insists that no more than 80 fans be produced during this production period. Resolve this product mix problem to find the new optimal solution. Let X 1 = the number of air conditioners scheduled to be produced X 2 = the number of fans scheduled to be produced Maximize 25X 1 + 15X 2 (maximize profit) Subject to: 3X 1 + 2X 2 240 (wiring capacity constraint) 2X 1 + X 2 140 (drilling capacity constraint) X 1 20 (a/c contract constraint) X 2 80 (maximum # of fans constraint) X 1 , X 2 0 (non-negativity constraints) Optimal Solution: X 1 = 40 X 2 = 60 Profit = $1,900
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ISM 6407 Fall 2009 7-16 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?
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This note was uploaded on 02/28/2012 for the course MGT 9650 taught by Professor Brooks during the Fall '11 term at CUNY Queens.

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LP Formulation Problems & Solutions - ISM 6407 Fall...

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