Lesson 3.8: Linear Programming

Question 1

Given constraints: x 0, y 0, 2x + 2y 4, x + y 8Explain the steps for maximizing the objective function P = 3x + 4y.

Revolt · Accepted Answer

To maximize the objective function, first graph the system of linear inequalities defined by the constraints to identify the feasible region. Next, determine the vertices (corner points) of this region by finding the intersection points of the boundary lines. Then, evaluate the objective function, P = 3x + 4y, at each of these vertices. Finally, compare the results; the vertex that produces the largest value is the point that maximizes the function.

Question 2

Did you include these steps in your answer? Check all of the boxes that apply.

Revolt · Accepted Answer

Graph the linear inequalities.; Find the vertices of the feasible region.; Evaluate the objective function at each vertex of the feasible region.; Find the point that results in the largest value

Question 3

✔ 10305070

Revolt · Accepted Answer

✔ 10

Question 4

⇒ 1130

Revolt · Accepted Answer

1130

Question 5

103050✔ 70

Revolt · Accepted Answer

✔ 70; The vertices of the feasible region are (70, 10), (30, 10), and (30, 50). To maximize the profit, the company should produce units of product A and units of product B. The maximum profit is $.: 70; The vertices of the feasible region are (70, 10), (30, 10), and (30, 50). To maximize the profit, the company should produce units of product A and units of product B. The maximum profit is $.: 10

Question 6

The graph shows the feasible region for the system with constraints:y [image 1] 15 x + y [image 2] 25 x + 2y [image 3] 30What are the vertices of the feasible region? Check all of the boxes that apply.

Revolt · Accepted Answer

(0, 15); (10, 15); (20, 5)

Question 7

ABC

Revolt · Accepted Answer

A

Question 8

A company produces two products, A and B. At least 30 units of product A and at least 10 units of product B must be produced. The maximum number of units that can be produced per day is 80. Product A yields a profit of $15 and product B yields a profit of $8. Let a = the number of units of product A and b = the number of units of product B.

Revolt · Accepted Answer

15; 15, 8

Question 9

What is the minimum value of the objective function C = 4x + 9y?C =

Revolt · Accepted Answer

PENDING

Question 10

x + y 800.4x + 0.5y 1006x + 4y 7202x + 4y 4006x + 2y 7204x + 4y 400

Revolt · Accepted Answer

x + y 80; 6x + 4y 720; 2x + 4y 400

Lesson 3.8: Linear Programming Answers

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