Linear Inequalities: Solving Real-World Problems

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. Graph the feasible region.

• A ≤ 2000, with x + y ≤ 25 and x, y ≥ 0.

• A ≤ 1000, with x + y ≤ 75 and x, y ≥ 0.

• A ≤ 1250, with x + y ≤ 50 and x, y ≥ 0.

• A ≤ 500, with x + y ≤ 100 and x, y ≥ 0.

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 a linear inequality to represent the number of students (x) that can attend the trip. Graph the feasible region.

• x ≤ 10

• x ≤ 20

• x ≤ 14

• x ≤ 5

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. Graph the feasible region.

• 2x + 3y ≥ 60

• x + y ≤ 20

• 2x + 3y ≤ 60

• 2x + 3y = 60

A restaurant sells two types of sandwiches: vegetarian and meat. The vegetarian sandwich costs $5 and the meat sandwich costs $7. If the restaurant wants to make at least $200 in one day, write a linear inequality to represent the sales of each type of sandwich. Graph the feasible region.

• 5x + 7y = 200

• 5x + 7y ≥ 200

• 5x + 7y > 200

• 5x + 7y ≤ 200

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 limits. Graph the feasible region.

• x + y ≥ 150

• x + y ≤ 150

• x + y < 150

• x + y = 150

A company produces two products, A and B. Each product A requires 4 hours of labor and each product B requires 2 hours. If the company has a maximum of 40 hours of labor available, write an inequality to represent the production limits. Graph the feasible region.

• 2x + 4y ≤ 40

• 3x + 2y ≤ 40

• 4x + 2y ≤ 40

• 4x + 3y ≤ 40

A charity event is selling tickets for $10 each and has a goal of raising at least $1,000. Write a linear inequality to represent the number of tickets (x) that need to be sold. Graph the feasible region.

• x < 100

• x <= 100

• x >= 100

• x > 100

A local bakery makes two types of cakes: chocolate and vanilla. Each chocolate cake requires 3 eggs and each vanilla cake requires 2 eggs. If the bakery has 30 eggs available, write an inequality to represent the maximum number of cakes that can be made. Graph the feasible region.

• 3x + 2y ≤ 30

• x + 2y ≤ 30

• 2x + 3y ≤ 30

• 3x + y ≤ 30

A clothing store sells shirts for $25 and pants for $40. If the store wants to make at least $1,200 in sales, write a linear inequality to represent the number of shirts (x) and pants (y) that need to be sold. Graph the feasible region.

• 25x + 40y ≤ 1200

• 30x + 35y ≥ 1200

• 25x + 40y ≥ 1200

• 25x + 40y = 1200

A concert venue has a seating capacity of 500. If x represents the number of VIP tickets sold and y represents the number of general admission tickets sold, write an inequality to represent the seating limits. Graph the feasible region.

• x + y < 500

• x + y ≥ 500

• x + y = 500

• x + y ≤ 500