Linear inequalities (two variables)

How many of each purse should Sarah make to maximize profit? (Recall: x represents small purses and y represents big purses)

• 6 big purses

• 8 small purses

• 6 small purses and 2 big purses

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

• 300
• 280
• 400
• 240

3. Katie works part-time at the Fallbrook Riding Stable. She makes $5 an hour for exercising horses and $10 an hour for cleaning stalls. Her goal is to make no less than $90 a week. Because Katie is a full-time student, she cannot work more than 12 hours per week and still maintain a high GPA. Write a system of equations that model this situation.

• 5x + 10y > 90

  x + y < 12

• 5x + 10y < 90

  x + y < 12

• 5x + 10y < 90

  x + y >12

• 5x + 10 > 90

  x + y < 12

Cole is doing a basketball challenge for charity. In order to win money for the charity, he needs to score at least 20 points in less than 10 shots. Which of these combinations of two- and three-point shots would allow Cole to beat the challenge? Select all that apply.

• 4 three-point baskets and 6 two-point baskets

• 5 three-point baskets and 1 two-point basket

• 7 three-point baskets and 8 two-point baskets

• 6 three-point baskets and 4 two-point baskets

Parker and Payton are also opening a pet-sitting business; they can fit a cat run in 5 square feet, and a dog run in 25 square feet. They cannot go over 250 square feet total.

Which of the following combinations of cats and dogs meet this constraint?

• 12 cats and 12 dogs

• 15 cats and 0 dogs

• 0 cats and 12 dogs

• 50 cats and 10 dogs

A company produces two types of products, Product P and Product Q. The profit per unit of Product P is $10 and the profit per unit of Product Q is $15. The company wants to maximize its profit while producing at least 50 units of Product P and at least 30 units of Product Q. Write a system of linear inequalities to represent this situation.

• 10x + 15y <= z

• x <= 50

• y <= 30

• 10x + 15y >= z x >= 50 y >= 30

Maximize P = 3x + y with the following constraints:

 $x+y\ \le300$ 

 $y\ \ge100$  

 $x\ \le150$  

• x = 0, y = 300

• x = 150, y = 150

• x = 100, y 150

• x = 150, y = 100

JoAnn likes her job as a baby-sitter, but it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. JoAnn wants to to tutor and baby-sit and make at least $66 per week. Formulate an system of inequalities to model how many hours per week she can work at each job.

• b + t < 15
  3b + 6t > 66
• b + t > 15
  3b + 6t < 66
• 3b + 6t > 15
  b + t < 66
• 3b + 6t < 15
  b + t < 66

4.)   John is going to the store to buy posters. Small posters cost $3.50 and large posters cost $6.00. He needs to buy at least 7 posters and can spend no more than $40.

Inequality 1: _______________

Inequality 2: _______________

Write the system of inequalities

Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing. Which is a possible solution?

• 300 adults and 0 children

• 200 adults and 1 children

• 100 adults and 100 children

• 300 adults and 100 children