Mth46t operations research - graph the region of feasible

Question

Assignment Questiom 1:

Graphically determine the feasible region (if one exists) for the following LP system.

2x₁ + 5x₂ ≤ 20

2x₁ + 2x₂ ≤ 24

2x₁ + x₂ = 10

x₁ ≥ 0

x₂ ≥ 0

Questiom 2

Graph the region of feasible solution (if one exists) and solve by corner-point method.

Maximixe z = 30 x + 20y

subject to 3x + y ≤ 18

                   x + y ≤ 12

                         x ≥  2

                         y ≥  5

                      x, y ≥  5