Graphing Systems of Inequalities: Feasible Regions Quiz

A farmer has 100 acres of land to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour of labor. If the farmer has a total of 120 hours of labor available, write a system of inequalities to represent the situation and identify the feasible region.

• x + 2y ≤ 100, 2x + 2y ≤ 120, x ≥ 0, y ≥ 0

• x + y ≤ 80, 2x + y ≤ 100, x ≥ 0, y ≥ 0

• x + y ≤ 100, 2x + y ≤ 120, x ≥ 0, y ≥ 0

• x + y ≤ 120, 2x + y ≤ 100, x ≥ 0, y ≥ 0

A school is planning a field trip and has a budget of $500. The cost per student for the trip is $20, and the bus rental costs $200. Write a system of inequalities to represent the number of students that can attend the trip and graph the feasible region.

• x ≥ 0 and x ≤ 12

• x ≥ 0 and x ≤ 15

• x ≥ 5 and x ≤ 20

• x ≥ 0 and x ≤ 10

A factory produces two types of toys: dolls and cars. Each doll requires 3 hours of labor and each car requires 2 hours. The factory has a maximum of 60 hours of labor available. Write the system of inequalities and identify the feasible region for the number of dolls and cars that can be produced.

• 4x + 2y ≤ 60, x ≥ 0, y ≥ 0

• 3x + y ≤ 60, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 60, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 60, x ≥ 0, y ≥ 0

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium membership costs $50 per month. If the gym wants to earn at least $1,200 in a month, write a system of inequalities to represent the number of each type of membership sold and graph the feasible region.

• 30x + 50y ≥ 1200, x ≥ 0, y ≥ 0

• 30x + 50y ≥ 1000, x ≥ 0, y ≥ 0

• 20x + 40y ≥ 1200, x ≥ 0, y ≥ 0

• 30x + 50y ≤ 1200, x ≥ 0, y ≥ 0

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 hours to bake, and each vanilla cake requires 1 hour. If the bakery has 10 hours available for baking, write a system of inequalities to represent the number of each type of cake that can be made and identify the feasible region.

• 2x + y ≤ 10, x ≥ 0, y ≥ 0

• 3x + y ≤ 10, x ≥ 0, y ≥ 5

• 2x + y ≥ 10, x ≥ 0, y ≥ 0

• x + 2y ≤ 10, x ≥ 0, y ≤ 0

A concert hall has a seating capacity of 500. Tickets for the front row cost $50 each, and tickets for the back row cost $30 each. If the concert hall wants to make at least $15,000 from ticket sales, write a system of inequalities and graph the feasible region for the number of front and back row tickets sold.

• x + y ≤ 500, 50x + 30y ≤ 15000, x ≥ 0, y ≥ 0

• x + y ≤ 500, 50x + 30y ≥ 15000, x ≥ 0, y ≥ 0

• x + y ≤ 600, 50x + 30y ≥ 10000, x ≥ 0, y ≥ 0

• x + y ≤ 400, 50x + 30y ≥ 20000, x ≥ 0, y ≥ 0

A pet store has a limit of 200 animals it can house. They have dogs and cats, with each dog taking up 3 units of space and each cat taking up 1 unit. Write a system of inequalities to represent the number of dogs and cats the store can have and identify the feasible region.

• 3x + y ≤ 200, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 200, x ≥ 0, y ≥ 0

• x + y ≤ 200, x ≥ 0, y ≥ 0

• 2x + y ≤ 200, x ≥ 0, y ≥ 0

A clothing store sells shirts and pants. Each shirt costs $15 and each pair of pants costs $25. If the store wants to make at least $1,000 in sales, write a system of inequalities to represent the number of shirts and pants sold and graph the feasible region.

• 10x + 20y >= 1000, x >= 0, y >= 0

• 15x + 30y >= 1000, x >= 0, y >= 0

• 20x + 25y >= 1000, x >= 0, y >= 0

• 15x + 25y >= 1000, x >= 0, y >= 0

A local charity is organizing a fundraiser and has a goal of raising at least $2,000. They plan to sell tickets for $10 each and donations of any amount. Write a system of inequalities to represent the number of tickets sold and the amount of donations received, and identify the feasible region.

• 10x + y >= 2000, x >= 0, y >= 0

• 5x + y >= 1500, x >= 0, y >= 0

• 10x + y >= 2500, x >= 0, y >= 0

• 10x + y <= 2000, x >= 0, y >= 0

A restaurant has a limit of 150 customers it can serve in a day. Each table can seat 4 people, and each booth can seat 6 people. Write a system of inequalities to represent the number of tables and booths the restaurant can use and graph the feasible region.

• 4x + 6y ≤ 150, x ≥ 0, y ≥ 0

• 3x + 5y ≤ 150

• x + y ≤ 50

• 2x + 4y ≤ 100