CO327W13_a4.pdf

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Department
Combinatorics and Optimization
Course
CO 250
Professor
Christine Dupont
Semester
Winter

Description
Assignment 4 Due: Wednesday March 20 at the BEGINNING of class 1. Consider the following LP: maximize 2x1+ x 2 x +33x + 4 ▯ x5 6 subject to x + 2x + x + x ▯ 2x = 3 1 2 4 5 6 ▯x 1 x ▯22x + 3x + x5 6 = 2 x ▯ x + x + x ▯ x + x = 1 1 2 3 4 5 6 x1;x 2x 3x 4x 5x 6 ▯ 0 (a) Give the canonical form of the LP for the basis B = f1;2;3g using tableau. (b) Using the tableau from part (a), perform the Dual Simplex Method to solve the LP. Give the optimal basis, the optimal solution and the optimal value. 2. Consider the following LP: maximize 200x 1 100x +2500x 3 subject to 10x + 20x + 40x ▯ 10000 1 2 3 25x 1 30x +250x 3 ▯ 25000 50x 1 40x +2100x 3 ▯ 40000 x ▯ 0 After converting to SEF by adding slack variables 4 ;x5;x6, the optimal tableau is: 2 3 1 0 120 0 5 0 3 170000 6 0 1 ▯2=5 0 ▯1=10 0 1=25 600 7 6 7 4 0 0 3=5 1
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