Real-World Linear Inequalities: Finding Feasible Regions

A farmer has 100 meters of fencing to create a rectangular pen for animals. If the length of the pen is represented by x meters and the width by y meters, write an inequality to represent the maximum area of the pen. What are the feasible dimensions?

• The feasible dimensions are 25 meters by 25 meters.

• 10 meters by 40 meters

• 15 meters by 35 meters

• 20 meters by 30 meters

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 an inequality to represent the maximum number of students that can attend. What is the feasible region for the number of students?

• x ≤ 20

• x ≤ 10

• x ≤ 5

• x ≤ 14

A factory produces two types of toys, A and B. Each toy A requires 2 hours of labor and each toy B requires 3 hours. If the factory has 60 hours of labor available, write an inequality to represent the production limits. What combinations of toys can be produced?

• The inequality is 2x + 3y ≤ 60, with combinations of (x, y) being non-negative integers satisfying this inequality.

• The inequality is 3x + 3y ≤ 60

• The inequality is 2x + 2y ≤ 60

• The inequality is 3x + 2y ≤ 60

A restaurant sells two types of sandwiches: chicken and veggie. Each chicken sandwich costs $5 and each veggie sandwich costs $4. If the restaurant wants to make at least $200 in one day, write an inequality to represent the sales. What are the possible combinations of sandwiches sold?

• 5x + 4y ≥ 200

• 3x + 2y ≥ 200

• 6x + 5y ≥ 200

• 5x + 4y ≤ 200

A gym has a maximum capacity of 150 members. If x represents the number of adult members and y represents the number of youth members, write an inequality to represent the membership limits. What combinations of adult and youth members are feasible?

• x - y ≤ 150

• x + y = 150

• x + y < 150

• x + y ≤ 150

A concert hall has 300 seats. If tickets for adults cost $10 and tickets for children cost $5, and the total revenue must be at least $2000, write an inequality to represent the ticket sales. What are the possible combinations of adult and child tickets sold?

• x + y ≥ 300 and 10x + 5y ≤ 2000

• x + y = 300 and 10x + 5y < 2000

• x + y ≤ 300 and 10x + 5y ≥ 2000, where x ≥ 0 and y ≥ 0.

• x + y ≤ 300 and 10x + 5y = 2000

A company produces two products, X and Y. Each product X requires 4 hours of machine time and each product Y requires 2 hours. If the machine is available for 40 hours, write an inequality to represent the production limits. What combinations of products can be produced?

• 4x + 2y ≥ 40

• The combinations of products X and Y that can be produced must satisfy the inequality 4x + 2y ≤ 40.

• 2x + 4y ≤ 40

• x + y ≤ 20

A charity event aims to raise at least $1000. If each ticket sold for adults is $15 and for children is $10, write an inequality to represent the ticket sales. What are the feasible combinations of adult and child tickets sold?

• 15x + 10y ≥ 1000, where x ≥ 0 and y ≥ 0.

• 15x + 10y ≤ 1000, where x ≥ 0 and y ≥ 0.

• 20x + 5y ≥ 1000, where x ≥ 0 and y ≥ 0.

• 10x + 15y ≥ 1000, where x ≥ 0 and y ≥ 0.

A local bakery can produce a maximum of 200 pastries in a day. If each pastry type A takes 3 minutes to make and type B takes 2 minutes, and the bakery operates for 8 hours, write an inequality to represent the production limits. What combinations of pastries can be made?

• 3x + 2y ≤ 480 and x + y ≤ 300

• 3x + 2y ≤ 400 and x + y ≤ 150

• 3x + 2y ≤ 600 and x + y ≤ 250

• The combinations of pastries can be represented by the inequalities: 3x + 2y ≤ 480 and x + y ≤ 200.

A clothing store has a sale on shirts and pants. Shirts cost $20 and pants cost $30. If the store wants to make at least $1000 in sales, write an inequality to represent the sales. What are the possible combinations of shirts and pants sold?

• 5x + 2y ≥ 100

• 2x + 3y ≥ 100

• 2x + 3y ≤ 100

• 2x + 3y = 100