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

c. (1 point) For this part only the objective function is Maximize 2x + 2y. Which of the following describes the optimal solution? (Put a check next to your answer) Infeasible solution Unique optimal solution Alternate optimal solution - Constraint 2 would be binding and has the same slope as the objective function Unbounded optimal solution

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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

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