Linear Inequalities in Two Variables and Linear Programming

For questions 3 - 6, use the following scenario: Suppose you can spend no more than 15 hours a week at your two jobs. Mowing lawns pays $3 an hour and babysitting pays $5 an hour. You need to earn at least $60 a week. Let x = # of hours mowing Let y = # of hours babysitting Which system of inequalities represents the scenario?

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 region represents more than $2000 made?

• Red

• Blue

• Purple (red and blue overlap)

• Non Shaded

Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Your tank can hold 14 gallons at most. Write a system to represent this situation.

• x+y≤14
  2x+3y≤18

• 2x+3y≤14
  x+y≤18

• 2x+y<18
  x+3y<14

• x+14≤y
  2x+3y≤18

A company produces two types of products, Product X and Product Y. The production time per unit of Product X is 4 hours and the production time per unit of Product Y is 6 hours. The company has a total of 30 hours of production time available. The company wants to produce at least 5 units of Product X and at least 4 units of Product Y. Write a system of linear inequalities to represent this situation.

• 4x + 6y >= 30, x <= 5, y <= 4.

• 4x + 6y <= 30, x >= 5, y >= 4

• 4x + 6y <= 30, x <= 5, y <= 4.

• 4x + 6y >= 30, x >= 5, y >= 4.

• Astrid meets both of her expectations

• Astrid buys the expected number of fruits, but she does beyond her budget

• Astrid stays within her budget, but she doesn't buy the expected number of fruits

• Astrid doesn't meet either of her expectations

• Lars meets both of his expectations

• Lars works for the expected number of days but doesn't earn the expected number of money

• Lars earns the expected amount of money but doesn't work for the expected number of days

• Lars doesn't meet either of his expectations

Lars meets both of his expectations

• Lars meets both of his expectations

• Lars works for the expected number of days but doesn't earn the expected number of money

• Lars earns the expected amount of money but doesn't work for the expected number of days

• Lars doesn't meet either of his expectations

The ordered pair (a)   is in the solution set of 8x+16y>32.

• (-3, 5)

• (0, 2)

• (-1, 1)

• (4, 0)

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

• 32

• 16

• 27

• 45

A company produces two products, Product A and Product B. The profit per unit of Product A is $5 and the profit per unit of Product B is $8. The company wants to maximize its profit while producing at least 100 units of Product A and at least 80 units of Product B. Write a system of linear inequalities to represent this situation.

• 5x + 8y ≥ 0, x ≥ 100, y ≥ 80

• 5x + 8y ≥ 0, x ≤ 100, y ≤ 80.

• 5x + 8y ≤ 0, x ≥ 100, y ≥ 80.

• 5x + 8y ≥ 0, x ≥ 50, y ≥ 80.