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3 years ago

Solve the linear programming problem.

Mathematics

1 answer:

larisa [96]3 years ago

7 0

Answer:

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.

Answer: 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.

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

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

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$(x - h)^2 + (y - k)^2 = r^2$

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Where:

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