IEOR162_hw08 - IEOR 162 Fall 2011 Homework 08 Note If an LP...

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IEOR 162, Fall 2011 Homework 08 Note. If an LP has n variables and m constraints (excluding nonnegativity constraints), its dual LP MUST have n constraints (excluding nonnegativity constraints) and m variables. 1. (Modified from Problem 6.3.6; 20 points) Sugarco can manufacture three types of candy bar. Each candy bar consists totally of sugar and chocolate. Fifty oz of sugar and 100 oz of chocolate are available. The compositions of each type of candy bar and the profit earned from each candy bar are shown in the table below. Amount of Amount of Profit Bar Sugar (Ounces) Chocolate (Ounces) (Cents) 1 1 2 3 2 1 3 7 3 1 1 5 After defining x i to be the number of type- i candy bars manufactured, Sugarco should solve the following LP: max 3 x 1 + 7 x 2 + 5 x 3 s.t. x 1 + x 2 + x 3 50 (Sugar constraint) 2 x 1 + 3 x 2 + x 3 100 (Chocolate constraint) x i 0 i = 1 , ..., 3 . After adding two slack variables, the optimal simplex tableau is shown below.
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