Consider the following linear optimization model: (P) min 2x1 +4x2+ 10x3 + 15x4 s.t. -x1 + x2 + x3 + 3x4 ≥ 1 x1x2 + 2x3 + x4 ≥ 1 X1, X2, x3, x4 ≥ 0. 1. Write a Phase-I model for (P). Add the slack/excess variables first (call them x5, x6) and then add two artificial variables. 2. Solve the Phase-I model using simplex. The starting basis of your Phase-I model should be compose of the two artificial variables. When selecting variables to enter the basis, always select the eligible variable with smallest index. When selecting variables to leave the basis, always select the eligible variable with smallest index. (When providing an answer to this problem, report (at least) the simplex dictionary obtained at each iteration, and state what variables are entering/leaving the basis.) At the conclusion of the algorithm, present the optimal solution you found.
Consider the following linear optimization model: (P) min 2x1 +4x2+ 10x3 + 15x4 s.t. -x1 + x2 + x3 + 3x4 ≥ 1 x1x2 + 2x3 + x4 ≥ 1 X1, X2, x3, x4 ≥ 0. 1. Write a Phase-I model for (P). Add the slack/excess variables first (call them x5, x6) and then add two artificial variables. 2. Solve the Phase-I model using simplex. The starting basis of your Phase-I model should be compose of the two artificial variables. When selecting variables to enter the basis, always select the eligible variable with smallest index. When selecting variables to leave the basis, always select the eligible variable with smallest index. (When providing an answer to this problem, report (at least) the simplex dictionary obtained at each iteration, and state what variables are entering/leaving the basis.) At the conclusion of the algorithm, present the optimal solution you found.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 6EQ: Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of...
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