Solve the following linear programming model graphically:

Maximize Z = 5x  ₁   + 8x  ₂ 

Subject to

3x  ₁   + 5x  ₂   ≤ 50

2x  ₁   +4x  ₂    ≤ 40

x  ₁   ≤ 8

x  ₂   ≤ 10

x  ₁  , x  ₂   ≤ 0

Shade the feasible region.

What are the extreme points? Give their (x1, x2)-coordinates.

Plot the objective function on the graph to demonstrate where it is optimized.

What is the optimal solution?

What is the objective function value at the optimal solution?