Graphing Systems of Inequalities: Real-World Scenarios

A farmer has a total of 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 of labor. If he has a maximum of 240 hours of labor available, write a system of inequalities to represent the situation and graph the feasible region.

• x + y ≤ 100, 2x + 4y ≤ 240, x ≥ 0, y ≥ 0

• x + y ≤ 100, 2x + 3y ≤ 240, x ≥ 0, y ≥ 0

• x + y ≤ 120, 2x + 3y ≤ 300, x ≥ 0, y ≥ 0

• x + y ≤ 80, 2x + 2y ≤ 240, x ≥ 0, y ≥ 0

A school is organizing a field trip and has a budget of $500. The cost per student for the trip is $20, and the bus rental costs $200. Write a system of inequalities to represent the number of students that can attend the trip and graph the solution set.

• 10x + 200 <= 500 and x >= 0

• The system of inequalities is: 20x + 200 <= 500 and x >= 0.

• 20x + 200 >= 500 and x <= 0

• 20x + 200 = 500 and x > 0

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 4 hours of labor and each Type B gadget requires 2 hours. The company has a maximum of 40 hours of labor available. Write a system of inequalities to represent the production limits and graph the feasible region.

• 5x + y ≤ 40, x ≥ 0, y ≥ 0

• 3x + 4y ≤ 40, x ≥ 0, y ≥ 0

• 4x + 2y ≤ 40, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 40, x ≥ 0, y ≥ 0

A restaurant offers two types of meals: vegetarian and non-vegetarian. The vegetarian meal costs $10 and the non-vegetarian meal costs $15. If the restaurant wants to make at least $300 in a day and can serve a maximum of 40 meals, write a system of inequalities and graph the solution set.

• 10x + 15y <= 300

• x + y >= 40

• The system of inequalities is: 10x + 15y >= 300, x + y <= 40, x >= 0, y >= 0.

• x <= 0, y <= 0

A clothing store sells shirts and pants. Each shirt costs $25 and each pair of pants costs $40. The store wants to make at least $1000 in sales and can sell a maximum of 30 items. Write a system of inequalities and graph the solution set.

• 25x + 40y >= 500, x + y <= 20, x >= 0, y >= 0

• 25x + 40y >= 1000, x + y >= 30, x < 0, y < 0

• The system of inequalities is: 25x + 40y >= 1000, x + y <= 30, x >= 0, y >= 0.

• 25x + 40y <= 1000, x + y >= 30, x >= 0, y >= 0

A charity event is selling tickets for adults and children. Adult tickets cost $15 and children tickets cost $10. The event aims to raise at least $2000 and can sell a maximum of 200 tickets. Write a system of inequalities and graph the feasible region.

• The system of inequalities is: 15x + 10y >= 2000, x + y <= 200, x >= 0, y >= 0.

• 15x + 10y <= 2000, x + y <= 150, x >= 0, y >= 0

• 15x + 10y >= 2000, x + y >= 200, x < 0, y >= 0

• 15x + 10y <= 2000, x + y >= 200, x >= 0, y >= 0

A tech company is developing two products: Product X and Product Y. Each Product X requires 5 hours of development and each Product Y requires 3 hours. The company has a maximum of 60 hours available for development. Write a system of inequalities to represent the production limits and graph the solution set.

• 5x + 3y ≥ 60, x ≥ 0, y ≥ 0

• 2x + 4y ≤ 60, x ≥ 0, y ≥ 0

• The system of inequalities is: {5x + 3y ≤ 60, x ≥ 0, y ≥ 0}

• 5x + 2y ≤ 60, x ≥ 0, y ≥ 0

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 hours to bake and each vanilla cake requires 3 hours. The bakery has a maximum of 30 hours available for baking. Write a system of inequalities and graph the feasible region.

• 2x + 3y ≥ 30, x ≤ 0, y ≤ 0

• The system of inequalities is: 2x + 3y ≤ 30, x ≥ 0, y ≥ 0.

• x + y ≤ 10, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 30, x ≥ 0, y ≤ 0

A concert venue has a maximum capacity of 500 people. Tickets for adults cost $50 and tickets for children cost $30. The venue wants to earn at least $20,000 from ticket sales. Write a system of inequalities to represent the situation and graph the solution set.

• x + y < 500, 50x + 30y < 20000

• x + y ≤ 500, 50x + 30y ≥ 20000

• x + y ≥ 500, 50x + 30y ≤ 20000

• x + y ≤ 500, 50x + 30y = 20000