Constraints Systems of Inequalities

Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the maximum value?

• maximum value at (5, 4); 32

• maximum value at (0, 8); 16

• maximum value at (9, 0); 27

• maximum value at (0, 0); 0

Which point is a solution?

• (0, 6)

• (-3, 4)

• (1, 0)

• (-4, 3)

You graph using Desmos.com and get the following graph. Which are vertices of the feasible region?

• (0, 0), (0, 6),

  (6, 2), (8, 0)

• (0, 0), (6, 0),

  (2, 6), (0, 8)

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.

Which inequality represents the situation?

• x + y ≤ 8

• x + y > 8

• 2x + 3y ≤ 6

• x + y ≤ 10

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18

• x + y ≤ 6

• x + y ≤ 9

• 3x + 2y ≤ 18

Due to the face that Sarah cannot make a negative number of purses, what other constraints does she have?

• x≥0

• y≥0

• x≤0

• y≤0

Which inequality is shown in the graph?

• y < 3x - 2

• y > 3x - 2

• y ≤ 3x - 2

• y ≥ 3x - 2

Which system of inequalities does the graph represent?

• y > x + 2

  y > -x - 1

• y > x + 2

  y < -x - 1

• y < x + 2

  y > -x - 1

• y < x + 2

  y < -x - 1

Consider the production constraints for x number of toy cars and y number of toy trucks.
The company has no more than 360 wheels in stock. Each toy car needs 4 wheels, and each toy truck needs 6 wheels.

This constraint is represented by the inequality 4x + 6y ≤ 360.

What is the maximum number of toy trucks the company can produce if no toy cars are produced?

• • 50

• • 60

• • 90

• • 100

Consider the production constraints for x number of toy cars and y number of toy trucks.
The company has no more than 360 wheels in stock. Each toy car needs 4 wheels, and each toy truck needs 6 wheels.

This constraint is represented by the inequality 4x + 6y ≤ 360.

What is the maximum number of toy cars the company can produce if no toy trucks are produced?

• • 50

• • 60

• • 90

• • 100