Consider the following linear programming problem P Maximize z 6 x 1 4 x 2 Subject to x 1 x 2 8 (1) 2 x 1 2 x 2 8 (2) x 1 x 2 2 (3) x 1 0 x 2 unconstrained in sign Let the slack of constraint (1) and (2) be x 3 and x 4 , respectively, and the surplus of constraint (3) be x 5 Answer the following independent questions What is the optimal solution, if (i) constraint (3) is removed from the formulation (ii) constraint (2) is removed from the formulation

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Question: Consider the following linear programming problem P : Maximize z = 6 x 1 + 4 x 2 Subject to x 1 + x 2

Consider the following linear programming problem P:

Maximize z = 6x₁ + 4 x₂

Subject to x₁ + x₂ 8 (1)

2x₁-2 x₂ 8 (2)

x₁ - x₂ 2 (3)

____________________________________

x₁ 0

x₂unconstrained in sign

Let the slack of constraint (1) and (2) be x₃ and x₄, respectively, and the surplus of constraint (3) be x₅. Answer the following independent questions:

What is the optimal solution, if

(i) constraint (3) is removed from the formulation?

(ii) constraint (2) is removed from the formulation?

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