Linear Inequalities Represent Constraints

Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Your tank can hold 14 gallons at most. Write a system to represent this situation.

• x+y≤14
  2x+3y≤18

• 2x+3y≤14
  x+y≤18

• 2x+y<18
  x+3y<14

• x+14≤y
  2x+3y≤18

A college student has two different jobs. Her comnbined work schedules consist of no more than 48 hours in one week.

Which graph best represents the solution set for all possible combinations of x, the number of hours she worked at her first job, and y, the number of hours she worked at her second job, in one week?

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A company produces two types of products, Product X and Product Y. The production time per unit of Product X is 4 hours and the production time per unit of Product Y is 6 hours. The company has a total of 30 hours of production time available. The company wants to produce at least 5 units of Product X and at least 4 units of Product Y. Write a system of linear inequalities to represent this situation.

• 4x + 6y >= 30, x <= 5, y <= 4.

• 4x + 6y <= 30, x >= 5, y >= 4

• 4x + 6y <= 30, x <= 5, y <= 4.

• 4x + 6y >= 30, x >= 5, y >= 4.

Abigail, Ethan, and Ava are planning a trip and they have different constraints on their budgets, time, and destinations. How do they determine a common solution to their system of inequalities?

• They graph each person's constraints and find the overlapping region that satisfies all

• They ignore the inequalities and find the average of their constraints

• They use trial and error to find a random solution that might satisfy all

• They solve a single person's constraints and apply the solution to the other people's constraints

Colin needs to save at least $200 for homecoming. He works 2 jobs earning $9/hour at Wawa and $25/hour mowing lawns. He only has time to work 16 hours before homecoming.

• x + y ≥ 25

  x + y ≤ 9

• 100x + 25 y ≤ 200

  2x + 9y ≤ 16

• x + y ≥ 200

  9x + 25y ≤ 16

• 9x + 25y ≥ 200

  x + y ≤ 16

Since Lexie can’t make a negative number of cobblers or pies, what additional constraints exist on our variables? Select all that apply.

• 7 candy bars &

  3 shirts

• 9 candy bars &

  1 shirt

• 5 candy bars &

  1 shirt

• 1 candy bar &

  10 shirts

• 4 candy bars &

  4 shirts

JoAnn likes her job as a baby-sitter, but it pays only $5 per hour. She has been offered a job as a tutor that pays $12 per hour. Because it's summer, her parents insist she works a minimum of 20 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $90 per week? How much does she make?

• b + t > 20 
  5b + 12t > 90

• b + t > 20 
  5b + 12t < 90

• 5b + 12t > 20
  b + t < 90

• 5b + 12t < 20 
  b + t < 90

A company produces two products, Product A and Product B. The profit per unit of Product A is $5 and the profit per unit of Product B is $8. The company wants to maximize its profit while producing at least 100 units of Product A and at least 80 units of Product B. Write a system of linear inequalities to represent this situation.

• 5x + 8y ≥ 0, x ≥ 100, y ≥ 80

• 5x + 8y ≥ 0, x ≤ 100, y ≤ 80.

• 5x + 8y ≤ 0, x ≥ 100, y ≥ 80.

• 5x + 8y ≥ 0, x ≥ 50, y ≥ 80.

Chef Ben is going to make several chocolate cakes and sponge cakes, where each chocolate cakes needs 5 eggs and each sponge cake needs 7 eggs. Chef Ben plan to make not more than 7 chocolate cakes and at least 3 sponge cakes. He can make a profit of $6 and $3 from selling each chocolate and each sponge cake respectively. He wants to earn the maximum profit but there are only 70 eggs available.

How many sponge cakes does Chef Ben need to sell to maximize profits?

• 0

• 3

• 10

• 5