Question

Consider the following constraints and the c g graph below: Constraint L:4x-y21 Constraint 2: x+ys4 Constraint 3:-x-4y 2-8 x, y20 4x-y=1 x-4y -8 a. (2 points) Shade the feasible region in the graph provided above. b. (1 point) For this part only the objective function is Minimize -2x + y. Which of the following describes the optimal solution? (Put a check next to your answer) Infeasible solution Unique optimal solution the point (4,0) minimizes the LP Alternate optimal solution Unbounded optimal solution

Answer 1

a)

4x-y=1 right side of the area of the line is the region for the optimal solution

x+y=4 left the side of the area of the line is the region for the optimal solution

-x-4y=-8 left the side of the area of the line is the region for the optimal solution

The shown shaded region is correct

b)

MInimize Z = -2x+y

optimal endpoint are the (0.25,0) , (0.706, 1.824), (2.667, 1.333) . and (4,0)

at (0.25,0), Z =-0.5

at (0.706, 1.824), Z = 0.412

at (2.667, 1.333), Z = -4.001

at (4,0), Z = -8

The unique optimal solution the point (4,0) minimizes the L.P

c) Maximize Z = 2x+2y

at (0.25,0), Z =0.5

at (0.706, 1.824), Z = 5.06

at (2.667, 1.333), Z = 8.982

at (4,0), Z = 8

but as constraint 2 x+y <=4 has same slope as 2x+2y

Alternate optimal solution - constraint 2 ...... fuction