Graphing Systems of Inequalities: Feasible Regions Quiz

A farmer has 100 meters of fencing to create a rectangular pen for sheep. The length of the pen must be at least twice the width. Write a system of inequalities to represent the possible dimensions of the pen. What is the feasible region for the dimensions?

• l + w ≤ 50, l ≥ 2w; feasible region is the area satisfying these inequalities.

• l + w = 100, l = w

• l + w ≥ 50, l ≤ 2w

• l + w ≤ 100, l ≥ w

A bakery sells two types of cakes: chocolate and vanilla. The bakery can make a maximum of 50 cakes in a day. The number of chocolate cakes must be at least 10 more than the number of vanilla cakes. Write a system of inequalities to represent the production limits. Identify the feasible region for cake production.

• x + y ≤ 40, x ≥ y

• x + y ≥ 50, x ≤ y + 10

• x + y = 50, x = y + 5

• x + y ≤ 50, x ≥ y + 10

A gym offers two types of memberships: basic and premium. The gym can accommodate a maximum of 200 members. The number of premium members must be at least 30% of the total members. Write a system of inequalities to represent the membership limits. What is the feasible region for memberships?

• x + y ≤ 150, y ≥ 70

• x + y < 200, y < 60

• x + y = 250, y ≥ 50

• x + y ≤ 200, y ≥ 60

A company produces two products, A and B. The production of product A requires 2 hours of labor and product B requires 3 hours. The company has a maximum of 60 hours of labor available. Additionally, the company wants to produce at least 10 units of product A. Write a system of inequalities to represent the production constraints. Identify the feasible region for production.

• 2x + 3y ≤ 50, x ≥ 5, y ≥ 0

• The system of inequalities is: 2x + 3y ≤ 60, x ≥ 10, x ≥ 0, y ≥ 0.

• x + 2y ≤ 60, x ≥ 10, y ≥ 0

• 2x + 3y ≤ 60, x ≥ 0, y ≥ 0

A concert venue can hold a maximum of 300 people. Tickets for adults cost $25 and tickets for children cost $10. The venue wants to sell at least 50 adult tickets. Write a system of inequalities to represent the ticket sales. What is the feasible region for ticket sales?

• x + y ≤ 250, x ≥ 50, y ≥ 0

• x + y ≤ 300, x ≥ 50, x ≥ 0, y ≥ 0

• x + y ≤ 300, x ≥ 50, y ≤ 100

• x + y ≤ 300, x ≥ 100, y ≥ 0

A charity organization is organizing a fundraiser and has a goal of raising at least $1,000. Each ticket sold for the event costs $50, and they also plan to sell raffle tickets for $5 each. Write a system of inequalities to represent the fundraising goal. Identify the feasible region for ticket sales.

• 50x + 5y ≤ 1000, x ≥ 0, y ≥ 0

• The system of inequalities is: 50x + 5y ≥ 1000, x ≥ 0, y ≥ 0.

• 50x + 5y ≥ 500, x ≥ 0, y ≥ 0

• 50x + 5y = 1000, x > 0, y > 0

A clothing store sells shirts and pants. The store has a maximum of 150 items to sell. The number of shirts must be at least 30 more than the number of pants. Write a system of inequalities to represent the inventory limits. Identify the feasible region for clothing sales.

• x + y >= 150, x <= y + 30, x >= 0, y >= 0

• x + y <= 100, x >= y + 20, x >= 0, y >= 0

• x + y <= 150, x <= y + 30, x >= 0, y >= 0

• x + y <= 150, x >= y + 30, x >= 0, y >= 0

A tech company is developing two products, X and Y. Each product requires a different amount of resources. Product X requires 4 units of resource A and 2 units of resource B, while product Y requires 3 units of resource A and 5 units of resource B. The company has a maximum of 100 units of resource A and 80 units of resource B available. Write a system of inequalities to represent the resource constraints. Identify the feasible region for product development.

• 4x + 2y ≤ 100, 3x + 5y ≤ 80, x ≥ 0, y ≥ 0

• 5x + 3y ≤ 100, 2x + 4y ≤ 80, x ≥ 0, y ≥ 0

• 4x + 5y ≤ 100, 2x + 3y ≤ 80, x ≥ 0, y ≥ 0

• 4x + 3y ≤ 100, 2x + 5y ≤ 80, x ≥ 0, y ≥ 0