Inequalities in Real Life: Writing & Finding Feasible Regions

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 an inequality to represent the maximum area of the pen. What is the feasible region for the dimensions of the pen?

• x + y ≤ 50, x ≥ 0, y ≥ 0

• x + y ≤ 100, x ≥ 0, y ≥ 0

• x + y ≤ 50, x < 0, y ≥ 0

• x + y < 50, x ≥ 0, y ≥ 0

A school is planning a field trip and has a budget of $500. If each student ticket costs $15 and each teacher ticket costs $20, write an inequality to represent the number of tickets that can be purchased. What is the feasible region for the number of students and teachers?

• 15x + 20y ≤ 500, x ≥ 0, y ≥ 0

• 20x + 15y ≤ 500

• 15x + 25y ≤ 500

• 10x + 15y ≤ 500

A factory produces two types of toys: type A and type B. Each type A toy requires 2 hours of labor and each type B toy requires 3 hours. If the factory has 60 hours of labor available, write an inequality to represent the production limits. What is the feasible region for the number of toys produced?

• 2x + 3y ≤ 60

• 4x + 2y ≤ 60

• 2x + 3y ≥ 60

• x + y ≤ 20

A restaurant can serve a maximum of 200 customers in a day. If each table can seat 4 customers and there are x tables, write an inequality to represent the maximum number of customers. What is the feasible region for the number of tables?

• 4x ≤ 150; 0 ≤ x ≤ 40

• 4x < 200; 0 < x < 50

• 4x ≤ 200; 0 ≤ x ≤ 50

• 4x ≥ 200; 0 ≤ x ≤ 100

A charity event aims to raise at least $1,000. If each ticket sold is $25 and each donation is $50, write an inequality to represent the fundraising goal. What is the feasible region for the number of tickets and donations?

• 25x + 50y = 1000

• 25x + 50y > 1000

• 25x + 50y <= 1000

• 25x + 50y >= 1000

A gym has a maximum capacity of 150 members. If x represents the number of adult members and y represents the number of child members, write an inequality to represent the membership limit. What is the feasible region for the number of adult and child members?

• x + y ≤ 150; feasible region: x ≥ 0, y ≥ 0, x + y ≤ 150

• x + y < 150; feasible region: x < 0, y < 0, x + y < 150

• x + y = 150; feasible region: x > 0, y > 0, x + y = 150

• x + y ≥ 150; feasible region: x ≥ 0, y ≥ 0, x + y ≥ 150

A company produces two products, A and B. Each product A requires 3 hours of machine time and each product B requires 2 hours. If the machine is available for 24 hours, write an inequality to represent the production constraints. What is the feasible region for the number of products produced?

• 2x + 3y ≤ 24

• 3x + 2y = 24

• 3x + 2y ≥ 24

• 3x + 2y ≤ 24

A concert hall has a seating capacity of 500. If each ticket for adults costs $30 and for children costs $15, write an inequality to represent the maximum revenue. What is the feasible region for the number of adult and child tickets sold?

• x + y < 500, x ≥ 0, y ≥ 0

• x + y ≤ 500, x ≥ 0, y ≥ 0

• x + y ≤ 500, x < 0, y ≥ 0

• x + y ≤ 600, x ≥ 0, y ≥ 0

A local bakery can produce a maximum of 300 pastries in a day. If each pastry type A takes 2 hours to make and type B takes 1 hour, write an inequality to represent the production time. What is the feasible region for the number of each pastry type?

• 2x + y ≤ 12 and x + y ≤ 150

• The inequalities are 2x + y ≤ 24 and x + y ≤ 300.

• 2x + y ≥ 24 and x + y ≥ 300

• x + 2y ≤ 24 and x + y ≤ 200

A clothing store has a sale on shirts and pants. If each shirt costs $20 and each pair of pants costs $30, and the total budget for clothing is $600, write an inequality to represent the spending limit. What is the feasible region for the number of shirts and pants purchased?

• 10x + 15y ≤ 600

• 20x + 30y ≥ 600

• 20x + 30y ≤ 600

• 20x + 30y = 600