Tutorial_8 - toys. The company can at most produce 28000...

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IELM202 Tutorial 8 1/6/11 1. The Toys-R-4-U Company has developed two new toys for possible inclusion in its product line for the upcoming Christmas season. Setting up the production facilities to begin production would cost $50,000 for toy 1 and $80,000 for toy2. Once these costs are covered, the toys would generate a unit profit of $10 for toy 1 and $15 for toy 2. The company has three factories that are capable of producing these toys. However, to avoid doubling the start-up costs, just one factory would be used, where the choice would be based on maximizing profit. For administrative reasons, the same factory would be used for both new toys if both are produced. Toy 1 can be produced at the rate of 50 per hour in factory 1 and 40 per hour in factory 2 and 50 per hour in factory 3. Toy 2 can be produced at the rate of 40 per hour in factory 1 and 25 per hour in factory 2 and 25 per hour in factory 3. Factories 1, 2 and 3, respectively, have 500 hours, 700 hours, and 800 hours of production time available before Christmas that could be used to produce these
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Unformatted text preview: toys. The company can at most produce 28000 units of toy 1and 20000 units of toy2. It is not known whether these two toys would be continued after Christmas. Therefore, the problem is to determine how many units (if any) of each new toy should be produced before Christmas to maximize the total profit. Formulate an IP model for this problem. Ans: Let X 1 , X 2 be the number of toys 1 and 2 produced Let Y 1 , Y 2 be binary variables indicating whether or not toys 1 and 2 are produced. Ex. Y 1 =1 if toy 1 is produced and Y 1 = 0 if toy 1 is not produced Let = otherwise factory Z i if 1 i is used ( i=1, 2, 3) IP: Max 2 1 2 1 80000 50000 15 10 y y x x--+ s.t. 1 1 28000 y x ≤ 2 2 20000 y x ≤ ) 1 ( 500 025 . 02 . 1 2 1 z M x x-+ ≤ + ) 1 ( 700 04 . 025 . 2 2 1 z M x x-+ ≤ + ) 1 ( 800 04 . 02 . 3 2 1 z M x x-+ ≤ + 1 3 2 1 ≤ + + z z z x 1 , x 2 ≥ 0 and integer y 1, y 2, Z i are binary variables ( i=1, 2, 3) 2. Midterm review...
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This note was uploaded on 01/05/2011 for the course IELM IELM202 taught by Professor D during the Fall '10 term at HKUST.

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