Consider a pair of dual LPs.none of the other four.The primal is feasible if and only if the dual is feasible.The primal is unbounded if and only if the dual is unbounded.The primal is infeasible if and only if the dual is infeasible.The primal has an optimal solution if and only if the dual has an optimalsolution.

The primal is feasible if and only if the dual is feasible. True. In linear programming, if the…

Answered: Consider a pair of dual LPs. none of…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 27EQ

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Consider the following linear program: Max Z = -4x1 + 2x2 Subject To: -2x1 + 2x2 ≤ 7 x1 ≥ 2 x1 - 4x2 ≤ 0 2x1 + 2x2 ≥ 10 x1, x2 ≥ 0 Part A: Write the LP in standard equality form. Part B: Solve the original LP graphically (to scale). Clearly identify the feasible region and, if one or more exist, the optimal solution(s) (provide exact values for x1, x2, and Z).
Solve the following linear optimization model using the Simplex Algorithm:Maximize z(x1, x2) = 3x1 + 2x2Subject to2x1 + 2x2 ≤ 82x1 + 1x2 ≤ 6x1, x2 ≥ 0
Prove that if a canonical LP problem has two optimal solutions then it has an infinite number of optimal solutions.
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