Graphing Linear Inequalities: Feasible Regions Explored

A local bakery sells cupcakes and cookies. Each cupcake costs $2 and each cookie costs $1. If the bakery wants to make at least $50 in one day, write a linear inequality to represent the situation. What is the feasible region on a graph for the number of cupcakes (x) and cookies (y) they can sell?

• 2x + 3y >= 50

• 3x + y >= 50

• 2x + y >= 50

• x + 2y <= 50

A school is planning a field trip and has a budget of $300. The cost per student is $15 for the trip. Write a linear inequality to represent the maximum number of students (x) that can attend. Graph the inequality and identify the feasible region.

• x ≤ 15

• x ≤ 10

• x ≤ 20

• x ≤ 25

A farmer has 100 acres of land to plant corn and wheat. Each acre of corn requires 2 hours of labor, and each acre of wheat requires 1 hour. If the farmer has 120 hours of labor available, write a linear inequality to represent the situation. What does the graph of this inequality look like?

• 3x + y <= 100

• 2x + y <= 120, x + y <= 100

• x + 2y <= 120

• 2x + 3y <= 120

A gym offers two types of memberships: a basic membership for $30 per month and a premium membership for $50 per month. If a customer can spend no more than $200 on memberships, write a linear inequality to represent the number of basic (x) and premium (y) memberships they can purchase. What is the feasible region?

• 30x + 50y < 200

• 30x + 50y ≤ 200

• 30x + 50y = 200

• 20x + 40y ≤ 200

A clothing store sells shirts for $20 and pants for $30. If the store wants to make at least $600 in sales, write a linear inequality to represent the number of shirts (x) and pants (y) they need to sell. Graph the inequality and identify the feasible region.

• 2x + 3y ≤ 60

• 2x + 3y ≥ 60

• x + y ≥ 20

• 2x + 3y = 60

A charity event is selling tickets for $10 each and donations are accepted. If they want to raise at least $500, write a linear inequality to represent the number of tickets sold (x) and the total donations (y). What does the graph of this inequality show?

• 10x + y = 500

• 5x + y >= 500

• 10x + y >= 500

• 10x + y <= 500

A concert venue has a seating capacity of 500. If tickets are sold for $25 each and VIP tickets for $50 each, and the venue wants to make at least $10,000, write a linear inequality to represent the number of regular tickets (x) and VIP tickets (y) sold. What is the feasible region on the graph?

• x + y = 500; 25x + 50y = 10000

• x + y ≤ 500; 25x + 50y ≥ 10000

• x + y ≤ 300; 25x + 50y ≥ 15000

• x + y ≥ 500; 25x + 50y ≤ 10000

A tech company produces laptops and tablets. Each laptop requires 3 hours of assembly and each tablet requires 2 hours. If the company has 60 hours available for assembly, write a linear inequality to represent the production limits. Graph the inequality and identify the feasible region.

• x + y ≤ 20

• 3x + 2y ≤ 60

• 3x + 2y ≥ 60

• 2x + 3y ≤ 60

A restaurant has a special offer for meals. Each meal costs $15 and drinks cost $5. If a family wants to spend no more than $100 on meals and drinks, write a linear inequality to represent the number of meals (x) and drinks (y) they can order. What does the graph of this inequality look like?

• 20x + 10y ≤ 200

• 15x + 10y ≤ 100

• 10x + 5y ≤ 80

• 15x + 5y ≤ 100

A landscaping company can plant trees and shrubs. Each tree takes 4 hours to plant and each shrub takes 2 hours. If the company has 40 hours available, write a linear inequality to represent the planting limits. Graph the inequality and identify the feasible region.

• 3x + 2y ≤ 40

• 4x + 3y ≤ 40

• 2x + 4y ≤ 40

• 4x + 2y ≤ 40