Mastering Graphing Linear Inequalities: Feasible Regions Quiz

1. A farmer has 100 meters of fencing to create a rectangular pen for his sheep. If the length of the pen is represented by x and the width by y, write the inequality that represents the maximum area he can enclose. Graph the inequality and identify the feasible region.

• x + y < 50, x > 0, y > 0

• x + y = 100, x ≥ 0, y ≥ 0

• x + y ≤ 50, x ≥ 0, y ≥ 0

• x + y ≤ 100, x ≥ 0, y ≥ 0

2. A school is planning a field trip and has a budget of $500. The cost per student is $20 for transportation and $15 for admission. Write the inequality that represents the number of students (x) that can attend the trip. Graph the inequality and identify the feasible region.

• x ≤ 5

• x ≤ 20

• x ≤ 14

• x ≤ 10

3. A company produces two types of gadgets, A and B. Each gadget A requires 2 hours of labor and each gadget B requires 3 hours. If the company has 30 hours of labor available, write the inequality for the production limits. Graph the inequality and identify the feasible region.

• 2x + 3y ≤ 30

• x + y ≤ 10

• 2x + 3y ≥ 30

• 2x + 3y = 30

4. A restaurant offers two types of meals: vegetarian and non-vegetarian. The vegetarian meal costs $10 and the non-vegetarian meal costs $15. If the restaurant wants to make at least $300 in a day, write the inequality and graph it to find the feasible region for the number of meals sold.

• x + y <= 30

• 3x + 2y >= 75

• 5x + 4y < 100

• The inequality is 2x + 3y >= 60.

5. A clothing store sells shirts and pants. Each shirt costs $25 and each pair of pants costs $40. If the store wants to make at least $1000 in sales, write the inequality and graph it to identify the feasible region for the number of shirts (x) and pants (y) sold.

• 25x + 40y = 1000

• 25x + 40y ≥ 1000

• 25x + 40y ≤ 1000

• 25x + 40y > 1000

6. A local gym has a maximum capacity of 50 members. If x represents the number of adult members and y represents the number of youth members, write the inequality that represents the gym's capacity. Graph the inequality and identify the feasible region.

• x + y ≤ 50

• x + y = 50

• x + y ≥ 50

• x + y < 50

7. A charity event is selling tickets for $10 each and has a goal of raising at least $2000. Write the inequality that represents the number of tickets (x) that need to be sold. Graph the inequality and identify the feasible region.

• x < 200

• x > 200

• x <= 200

• x >= 200

9. A student is saving money for a new laptop that costs $800. If she saves $50 a week, write the inequality that represents the number of weeks (x) she needs to save to afford the laptop. Graph the inequality and identify the feasible region.

• 50x = 800; x = 16

• 50x < 800; x < 16

• 50x >= 800; x >= 16

• 50x <= 800; x <= 16

10. A park is planning to plant trees and shrubs. Each tree costs $30 and each shrub costs $15. If the park has a budget of $600, write the inequality that represents the maximum number of trees (x) and shrubs (y) that can be planted. Graph the inequality and identify the feasible region.

• 20x + 10y ≤ 600

• 25x + 20y ≤ 600

• 15x + 30y ≤ 600

• 30x + 15y ≤ 600