Exploring Feasible Regions: Real-Life Inequalities Quiz

A farmer has 100 acres of land. He wants 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 he has a total of 120 hours of labor available, write a system of inequalities to represent the feasible region for the number of acres of corn (x) and wheat (y) he can plant.

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

• 2x + 3y ≤ 120

• x + y ≤ 80

• x + 2y ≤ 100

A school is organizing 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 determine the maximum number of students (x) that can attend the trip while staying within budget.

• x <= 20

• x <= 5

• x <= 10

• x <= 15

A company produces two types of gadgets: A and B. Each gadget A requires 3 hours of assembly and each gadget B requires 2 hours. The company has a maximum of 30 hours available for assembly. Write a system of inequalities to represent the number of gadgets A (x) and B (y) that can be produced.

• 3x + y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

• x + y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 30, x ≥ 0, y ≥ 0

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 pounds of flour and each vanilla cake requires 1 pound. If the bakery has 20 pounds of flour, write a system of inequalities to represent the number of chocolate (x) and vanilla (y) cakes that can be made.

• 2x + y ≤ 20, x ≥ 0, y ≥ 0

• 2x + y < 20, x ≥ 0, y ≥ 0

• 3x + y ≤ 20, x ≥ 0, y ≥ 0

• x + 2y ≤ 20, x ≥ 0, y ≥ 0

A concert hall has 200 seats. Tickets for the front row cost $50 each, and tickets for the back row cost $30 each. If the concert hall wants to earn at least $6000 from ticket sales, write a system of inequalities to represent the number of front row (x) and back row (y) tickets that can be sold.

• x + y ≥ 200, 50x + 30y = 6000

• x + y ≤ 150, 50x + 30y ≥ 5000

• x + y = 200, 50x + 30y ≤ 6000

• x + y ≤ 200, 50x + 30y ≥ 6000

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 $300 in sales, write a system of inequalities to represent the number of shirts (x) and pants (y) that can be sold.

• 15x + 30y >= 300, x >= 0, y >= 0

• 15x + 25y <= 300, x >= 0, y >= 0

• 10x + 20y >= 300, x >= 0, y >= 0

• 15x + 25y >= 300, x >= 0, y >= 0

A charity event is selling tickets for a dinner. Each ticket costs $40, and they want to sell at least 100 tickets to cover costs. Write a system of inequalities to represent the number of tickets (x) they need to sell to meet their goal.

• x <= 100, x >= 0

• x >= 50, x <= 150

• x >= 100, x >= 0

• x < 100, x >= 0

A local theater has 150 seats. They charge $10 for regular seats and $15 for premium seats. If they want to make at least $1200 from ticket sales, write a system of inequalities to represent the number of regular (x) and premium (y) seats that can be sold.

• x + y >= 150, 10x + 15y <= 1200

• x + y <= 100, 10x + 15y >= 1500

• x + y <= 150, 10x + 15y >= 1200

• x + y <= 150, 10x + 15y = 1000

A pet store has a limit of 50 animals it can house. They have dogs and cats, with each dog taking up 2 spaces and each cat taking up 1 space. If they want to house at least 20 animals, write a system of inequalities to represent the number of dogs (x) and cats (y) they can have.

• x + y <= 50, 2x + y >= 20

• x + 2y <= 50, x + y <= 20

• 2x + y >= 50, x + y <= 20

• 2x + y <= 50, x + y >= 20