Consider the following linear programming problem:

Min (12x₁+18x₂)

            X₁ + 2x₂ ≤ 40

            X₁ ≤ 50

            X₁ + X₂ = 40

            X₁,X₂ ≥ 0

The above constraints when plotted result in the diagram below.. ( sent as an image)

1.) The feasible region for the problems is:

A.) triangle ABC and inside

B.) problem is infeasible

C.) only at point B

D.) only at point D

2.) The optimum value of the objective function is:

A.) 120                                                            B.) 480

C.) 360                                                            D.) None of the above

The LP model is modified as follows:

Min (12x₁+18x₂)

            X₁ + 2x₂ ≤ 40

            X₁  ≥ 50

            X₁ + X₂ = 40

            X₁,X₂ ≥ 0

3.) The feasible region for the modified problem is:

A.) triangle ABC and inside

B.) problem is infeasible

C.) only at point B

D.) only at point D

The LP model is modified as follows:

The LP model is modified as follows:

Min (12x₁+18x₂)

            X₁ + 2x₂ = 40

            X₁ ≤ 50

            X₁ +X₂   ≥ 40

            X₁ +X₂   ≥ 0

Determine the feasible region.