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Consider the LPP in standard form of maximizing 1x₁ + 2x2 + 1x3 subject to the feasible set: x₁ + x2 + 4x3 ≤ 12, 6 ≥ x1 ≥ 0, x3 ≥ 0, and x₂ ≥ 0. (a) Obtain A and b by putting this problem in canonical form. Note: make sure your matrix A has linearly independent rows. (b) Find all the BFS and determine which BFS has the maximum cost? (c) Use the Simplex method to find the optimal solution x* to the canonical form problem in part (a). Hint: do you get the same answer as in part (b) ?

Consider the LPP in standard form of maximizing 1x₁ + 2x2 + 1x3 subject to the feasible set: x₁ + x2 + 4x3 ≤ 12, 6 ≥ x1 ≥ 0, x3 ≥ 0, and x₂ ≥ 0. (a) Obtain A and b by putting this problem in canonical form. Note: make sure your matrix A has linearly independent rows. (b) Find all the BFS and determine which BFS has the maximum cost? (c) Use the Simplex method to find the optimal solution x* to the canonical form problem in part (a). Hint: do you get the same answer as in part (b) ?

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
Problem 40E
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(3) Consider the LPP in standard form of maximizing 1x₁ + 2x2 + 1x3 subject to the feasible set: x₁ +x2 + 4x3 ≤ 12, 6 ≥ x₁ ≥ 0, x3 ≥ 0, and x2 ≥ 0. (a) Obtain A and b by putting this problem in canonical form. Note: make sure your matrix A has linearly independent rows. (b) Find all the BFS and determine which BFS has the maximum cost? (c) Use the Simplex method to find the optimal solution x* to the canonical form problem in part (a). Hint: do you get the same answer as in part (b) ?
Transcribed Image Text:(3) Consider the LPP in standard form of maximizing 1x₁ + 2x2 + 1x3 subject to the feasible set: x₁ +x2 + 4x3 ≤ 12, 6 ≥ x₁ ≥ 0, x3 ≥ 0, and x2 ≥ 0. (a) Obtain A and b by putting this problem in canonical form. Note: make sure your matrix A has linearly independent rows. (b) Find all the BFS and determine which BFS has the maximum cost? (c) Use the Simplex method to find the optimal solution x* to the canonical form problem in part (a). Hint: do you get the same answer as in part (b) ?
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