onsider 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)

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x₁ 0

x₂ unconstrained in sign

Let the slack of constraint (1) and (2) be x₃ and x₄, respectively, and the surplus of constraint (3) be x₅. 1Determine the optimal solution(s), if instead of maximization the objective was minimization.

2 For each one of the three points given by their coordinates (x₁, x₂) below, determine if the point is feasible or infeasible. If feasible, find out if any constraints are active (binding) at that point. If infeasible, indicate the violated constraint(s). Justify your answer by checking each constraint.

(4, 3)

(3, -1)

(4, 1)

3 Consider varying the right-hand side of constraint (3) from its current value (b₃ = 2). Determine

1. its lowest value below which the problem becomes redundant and

(b) its highest value beyond which the problem becomes infeasible.