4.3: Linear Programming Basics

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 ≤ 6
• 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

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective quantity?

• P = 30x + 50y
• P = 50x + 30y

Objective quantity:
P = 30x + 50y
Corner that maximizes profit: (0, 6)
What is the profit?

• 300
• 280
• 400
• 240

Which of the following inequalities matches the given graph?

• x ≥ -1
• x ≤ -1
• x > -1
• x < -1

Which of the following inequalities matches the given graph?

• y ≤ -3/4 x + 3

• y ≥ -3/4 x + 3

• y < -3/4 x + 3

• y > -3/4 x + 3

Which are vertices of the feasible region?

• (0, 3) (3, 0) (5, 8)

• (0, 6) (3, 5) (6, 5)

• (3, 3) (8, 5) (5, 8)

• (0, 5) (6, 0) (3, 3)

What do you call the area where all the shading overlaps?

• the answer

• the feasible region

• the void

• the objective function

Given the objective function: P = 30x + 50y

Which vertex maximizes the profit?

• (0,0)

• (6,2)

• (8,0)

• (0,6)

 $3x+2y\le12$  

What are the x and y-intercepts for the given inequality?

• (2, 0) and (0, 4)

• (-2, 0) and (0, -4)

• (4,0) and (0, 6)

• (6, 0) and (0, 4)