Solving Linear Inequalities: Feasible Regions in Real Life

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 inequality and identify the feasible region.

• 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. The cost per student is $20, and the total number of students is represented by x. Write an inequality to represent the number of students that can attend the trip. Solve the inequality and graph the feasible region.

• x ≤ 25

• x = 25

• x ≥ 30

• x < 20

A bakery sells cookies for $2 each and brownies for $3 each. If the bakery wants to make at least $100 in one day, write an inequality to represent the relationship between the number of cookies (x) and brownies (y) sold. Graph the inequality and identify the feasible region.

• x + y ≥ 50

• 2x + 3y ≤ 100

• 4x + 2y ≥ 100

• 2x + 3y ≥ 100

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 gym's capacity. Solve the inequality and graph the feasible region.

• x + y ≥ 150

• x + y ≤ 150

• x + y < 150

• x + y = 150

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 2 hours of labor, and each Type B gadget requires 3 hours. If the company has 24 hours of labor available, write an inequality to represent the production limits. Graph the inequality and identify the feasible region.

• 2x + 3y ≤ 24

• 3x + 2y ≤ 24

• x + 2y ≤ 24

• 2x + 3y ≥ 24

A local charity is organizing a fundraiser and needs to sell at least 200 tickets. If each adult ticket costs $10 and each child ticket costs $5, write an inequality to represent the total number of tickets sold. Solve the inequality and graph the feasible region.

• x + y > 200

• x + y >= 200

• x + y = 200

• x + y <= 200

A car rental company charges a flat fee of $50 plus $0.20 per mile driven. If a customer has a budget of $100, write an inequality to represent the maximum number of miles (x) they can drive. Graph the inequality and identify the feasible region.

• x <= 250

• x <= 150

• x <= 300

• x <= 200

A restaurant offers a special deal where a family can order a maximum of 5 pizzas and 10 drinks. If x represents the number of pizzas and y represents the number of drinks, write an inequality to represent this deal. Solve the inequality and graph the feasible region.

• x >= 5, y >= 10, x + y >= 15

• x <= 3, y <= 5, x + y <= 8

• x + y <= 10, x <= 4, y <= 6

• x <= 5, y <= 10, x + y <= 15

A clothing store has a sale where each shirt costs $15 and each pair of pants costs $25. If a customer has $200 to spend, write an inequality to represent the maximum number of shirts (x) and pants (y) they can buy. Graph the inequality and identify the feasible region.

• 5x + 30y ≤ 200

• 15x + 25y ≤ 200

• 20x + 15y ≤ 200

• 10x + 20y ≤ 200

A concert venue has a seating capacity of 300. 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 limit. Solve the inequality and graph the feasible region.

• x + y ≤ 300

• x + y = 300

• x + y < 300

• x + y ≥ 300