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Practice Questions - Linear Programming Answers

# Practice Questions - Linear Programming Answers - Practice...

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Practice Questions: Linear Programming 1. A steel manufacturer produces metal sheet in standard size of: width 11ft and length 11ft. After the production, the plant can cut the sheet into the sizes a customer may want. For example, it can cut a sheet into 2 pieces of 11ft*4ft and one piece of 11ft*3ft. A customer comes and need 100 11ft*3ft, 200 11ft*4ft, and 300 11ft*5ft sheets. What is the smallest number of metal sheets the company must produce to satisfy all the demand? In order to produce the 100 11ft*3ft, 200 11ft*4ft, and 300 11ft*5ft sheets from standard size 11ft*11ft sheet, the following cut pattern can be used. a. having 3 3ft one from one standard sheet b. having 2 3ft one and 1 4ft one from one standard sheet c. having 1 3ft one and 2 4ft one from one standard sheet d. having 2 3ft one and 1 5ft one from one standard sheet e. having 1 4ft one and 1 5ft one from one standard sheet f. having 2 5ft one from one standard sheet Assume we use x_1, x_2, x_3, x_4, x_5, x_6 sheets for all the six cutting pattern: Objective function : min x_1+x_2+x_3+x_4+x_5+x_6 Constraints: 3x_1+2x_2+x_3+2x_4>=100 x_2+2x_3+x_5>=200 x_4+x_5+2x_6>=300 The optimal solution is x_3=100, x_6=150, and all other xs equal to zero. 2. The Sue All Law Firm handles two types of lawsuits: medical malpractice suits against unscrupulous heart surgeons for performing unnecessary surgery, and suits against hard-working math professors for failing students who do not deserve to pass. Math professor lawsuits each require 6 person-months of preparation and the hiring of 5 expert witnesses, whereas medical lawsuits each require 10 person-months of preparation and the hiring of 3 expert witnesses. The firm has a total of 30 person-months to work with and feels that it cannot afford to hire more than 15 expert witnesses. It makes an average profit of \$1 million per math professor sued and \$5 million per heart surgeon sued. How many of each type of lawsuit should it initiate in order to maximize its expected profits? X :number of lawsuits against teachers Y :number of lawsuits against a medic

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Objective function: Max 1X + 5Y Constraints: 6X + 10Y <=30 5X + 3Y <= 15 X,Y >= 0 3. O'Hagan Bookworm Booksellers buys books from two publishers. Duffin House offers a package of 5 mysteries and 5 romance novels for \$50, and Gorman Press offers a package of 5 mysteries and 10 romance novels for \$150. O'Hagan wants to buy at least 2,500 mysteries and 3,500 romance novels, and he has promised Gorman (who has influence on the Senate Textbook Committee) that at least 25% of the total number of packages he purchases will come from Gorman Press. How many packages should O'Hagan order from each publisher in order to minimize his cost and satisfy Gorman? What will the novels cost him?
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Practice Questions - Linear Programming Answers - Practice...

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