Mastering Graphing and Writing Linear Inequalities

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 1 hour of labor. If he has a total of 120 hours of labor available, write a system of inequalities to represent the situation and graph the feasible region.

• x + y >= 100, 2x + y >= 120, x <= 0, y <= 0

• x + y <= 80, 2x + y <= 100, x >= 0, y >= 0

• x + y <= 120, 2x + y <= 150, x >= 0, y >= 0

• x + y <= 100, 2x + y <= 120, 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 feasible region.

• 20x + 150 <= 500, x >= 0

• 20x + 200 >= 500, x >= 0

• 20x + 200 <= 500, x >= 0

• 15x + 200 <= 500, x >= 0

A company produces two types of gadgets: Type A and Type B. Each Type A gadget requires 3 hours of assembly, and each Type B gadget requires 2 hours. The company has 30 hours of assembly time available. Write the inequalities that represent the production limits and graph the feasible region.

• 4x + y ≤ 30, x ≥ 0, y ≥ 0

• 2x + 3y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 2y ≤ 30, x ≥ 0, y ≥ 0

• 3x + 3y ≤ 30, x ≥ 0, y ≥ 0

A gym offers two types of memberships: basic and premium. The basic membership costs $30 per month, and the premium membership costs $50 per month. If the gym wants to earn at least $1,200 in a month, write a system of inequalities to represent the number of each type of membership sold and graph the feasible region.

• 30x + 50y = 1200, x >= 0, y >= 0

• 30x + 50y <= 1200, x >= 0, y >= 0

• 30x + 50y >= 1200, x >= 0, y >= 0

• 20x + 40y >= 1200, x >= 0, y >= 0

A bakery sells two types of cakes: chocolate and vanilla. Each chocolate cake requires 2 pounds of flour, and each vanilla cake requires 1 pound. The bakery has 10 pounds of flour available. Write the inequalities that represent the baking limits and graph the feasible region.

• 3x + y <= 10, x >= 0, y >= 0

• x + 2y <= 10, x >= 0, y >= 0

• 2x + y <= 10, x >= 0, y >= 0

• 2x + y >= 10, x >= 0, y >= 0

A concert hall has a seating capacity of 500. Tickets for the front row cost $50, and tickets for the back row cost $30. If the concert hall wants to earn at least $20,000 from ticket sales, write a system of inequalities to represent the ticket sales and graph the feasible region.

• x + y ≥ 500, 50x + 30y ≤ 20000

• x + y ≤ 400, 50x + 30y ≥ 25000

• x + y = 500, 50x + 30y = 20000

• x + y ≤ 500, 50x + 30y ≥ 20000

A clothing store sells shirts and pants. Each shirt costs $15, and each pair of pants costs $25. The store has a budget of $600 for inventory. Write a system of inequalities to represent the purchasing limits and graph the feasible region.

• 15x + 25y ≤ 500, x ≥ 0, y ≥ 0

• 10x + 20y ≤ 600, x ≥ 0, y ≥ 0

• 15x + 25y ≤ 600, x ≥ 0, y ≥ 0

• 15x + 30y ≤ 600, x ≥ 0, y ≥ 0

A charity event is selling two types of tickets: adult tickets for $15 and child tickets for $10. They want to raise at least $1,000. Write a system of inequalities to represent the ticket sales and graph the feasible region.

• 15x + 10y = 1000, x < 0, y < 0

• 10x + 15y ≥ 1000, x ≥ 0, y < 0

• 15x + 10y ≤ 1000, x ≥ 0, y ≥ 0

• 15x + 10y ≥ 1000, x ≥ 0, y ≥ 0

A restaurant offers two types of meals: vegetarian and non-vegetarian. Each vegetarian meal costs $12, and each non-vegetarian meal costs $15. If the restaurant wants to make at least $800 in a day, write a system of inequalities to represent the meal sales and graph the feasible region.

• 12x + 15y >= 800, x >= 0, y >= 0

• 12x + 15y <= 800, x >= 0, y >= 0

• 10x + 20y >= 800, x >= 0, y >= 0

• 12x + 15y >= 1000, x >= 0, y >= 0

A tech company is developing two products: a smartphone and a tablet. Each smartphone requires 4 hours of development, and each tablet requires 3 hours. The company has 36 hours available for development. Write the inequalities that represent the development limits and graph the feasible region.

• 2x + 5y ≤ 36, x ≥ 0, y ≥ 0

• 4x + 3y ≥ 36, x ≥ 0, y ≥ 0

• 4x + 3y ≤ 36, x ≥ 0, y ≥ 0

• x + y ≤ 12, x ≥ 0, y ≥ 0