Solve the linear programming problem. 1. Maximize: P = 4x +4y
Subject to: 2x + y ≤ 20
x + 2y ≤ 16
x, y ≥ 0

a. Find the maximum P= at x, y ( , )

2. Maximize P = 3x + 2y
Subject to x + y ≤ 8
2x + y ≤ 13
x ≥ 0, y ≥ 0

1. Objective function is a maximum at (16,0), Z = 4x+4y = 4(16) + 4(0) = 64

2. Objective function is at a maximum at (5,3), Z=3x+2y=3(5)+2(3)=21

Step-by-step explanation:

1. Maximize: P = 4x +4y

Subject to: 2x + y ≤ 20

x + 2y ≤ 16

x, y ≥ 0

Plot the constraints and the objective function Z, or P=4x+4y)

Push the objective function to the limit permitted by the feasible region to find the maximum.

Objective function is a maximum at (16,0),

              Z = 4x+4y = 4(16) + 4(0) = 64

2. Maximize P = 3x + 2y

Subject to x + y ≤ 8

2x + y ≤ 13

x ≥ 0, y ≥ 0

Plot the constraints and the objective function Z, or P=3x+2y.

Push the objective function to the limit in the increase + direction permitted by the feasible region to find the maximum intersection.

Objective function is at a maximum at (5,3),

              Z = 3x+2y = 3(5)+2(3) = 21