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IEOR162_hw06 - IEOR 162 Fall 2011 Homework 06 Whenever you...

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IEOR 162, Fall 2011 Homework 06 Whenever you do pivoting, use the smallest index rule. If you DO NOT follow the smallest index rule, you may have tableaus different the standard solution. This is treated as a WRONG solution process. 1. (10 points) Suppose you see the following tableau when you solve a maximization standard form LP with six variables x 1 , x 2 , ..., x 6 : - 2 0 0 0 0 - 5 36 4 0 - 2 0 1 3 12 0 1 0 0 0 - 2 2 3 0 - 1 1 0 - 4 9 (a) (2 points) Write down the basic feasible solution corresponding to the current tableau. Note that the basic feasible solution have six variables. (b) (2 points) Is the corresponding basic feasible solution degenerate? Why? (c) (3 points) Using the smallest index rule, determine the entering variable. (d) (3 points) Using the smallest index rule, determine the leaving variable. 2. (MODIFIED from Problem 4.11.1; 10 points) Consider the following linear program max 3 x 1 + 7 x 2 s.t. 2 x 1 + 4 x 2 12 x 1 + 4 x 2 10 x 1 + x 2 4 x i 0 i = 1 , 2 .
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