Grade 8 Inequalities: Modeling & Feasible Regions Quiz

A farmer has 100 acres of land. He wants to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 3 hours. If he has a total of 240 hours of labor available, write an inequality to represent the situation and identify the feasible region.

• x + y ≤ 100, 2x + 2y ≤ 240

• x + y ≤ 80, 2x + 3y ≤ 200

• x + y ≥ 100, 2x + 3y ≤ 240

• x + y ≤ 100, 2x + 3y ≤ 240

A school is planning a field trip and has a budget of $500. The cost per student for transportation is $10, and for admission, it is $15. Write an inequality to model the maximum number of students that can attend the trip and identify the feasible region.

• x ≤ 25

• x ≤ 15

• x ≤ 20

• x ≤ 30

A factory produces two types of toys: dolls and cars. Each doll requires 4 hours of labor, and each car requires 2 hours. If the factory has 80 hours of labor available, write an inequality to represent the production limits and identify the feasible region.

• 2x + y ≥ 40

• 3x + 2y ≤ 80

• x + y ≤ 20

• 2x + y ≤ 40, x ≥ 0, y ≥ 0

A gym offers two types of memberships: basic and premium. The basic membership costs $20 per month, and the premium membership costs $35 per month. If the gym wants to earn at least $1,000 in a month, write an inequality to model the situation and identify the feasible region.

• 20x + 35y ≥ 1000

• 25x + 40y ≤ 1000

• 20x + 35y = 1000

• 15x + 30y ≥ 1000

A bakery sells 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 and identify the feasible region.

• 3x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 4x + y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

A concert hall has a seating capacity of 500. If tickets for the front row cost $50 and tickets for the back row cost $30, and the total revenue must be at least $15,000, write an inequality to model the situation and identify the feasible region.

• x + y ≥ 500 and 50x + 30y ≤ 15000

• x + y = 500 and 50x + 30y = 15000

• x + y ≤ 500 and 50x + 30y ≥ 15000

• x + y ≤ 400 and 50x + 30y ≥ 20000

A pet store has a limit of 50 animals it can house. If each dog takes up 2 spaces and each cat takes up 1 space, write an inequality to represent the maximum number of dogs and cats the store can have and identify the feasible region.

• 3d + 2c ≤ 50

• d + c ≤ 50

• 2d + c ≤ 50

• d + 2c ≤ 50

A local community center has a budget of $1,200 for a new playground. If swings cost $200 each and slides cost $300 each, write an inequality to model the maximum number of swings and slides that can be purchased and identify the feasible region.

• 200x + 300y ≤ 1200

• 150x + 250y ≤ 1200

• 100x + 300y ≤ 1200

• 200x + 200y ≤ 1200

A clothing store sells shirts for $25 and pants for $40. If the store wants to make at least $2,000 in sales, write an inequality to represent the sales goal and identify the feasible region.

• 25x + 40y ≤ 2000

• 25x + 40y > 2000

• 25x + 40y ≥ 2000

• 25x + 40y = 2000

A garden center has 60 pots available for planting flowers and shrubs. If each flower requires 1 pot and each shrub requires 2 pots, write an inequality to represent the planting limits and identify the feasible region.

• 2x + y ≤ 60

• x + 3y ≤ 60

• x + 2y ≤ 60

• x + y ≤ 60