Consider the following linear programming problem: Max Z = - X 1 + X 2 Subject to (1)X 1 + X 2 = 2 (3)2X

Consider the following linear programming problem:

Max Z = - X₁ + X₂

Subject to

(1)X₁+ X₂ <= 5

(2)- X₁ + 3X₂ >= 2

(3)2X₁- X₂ <= 2

X₁, X₂ >= 0

a. Graph the constraint lines and mark them clearly with the numbers (1), (2), and (3) to indicate which line corresponds to which constraint. Darken the feasible region.

b. Determine the optimal solution that will maximize the objective function Z. Provide all necessary calculations to justify your answers.

c. Which constraint(s) is (are) non-binding? Justify