Linear Programming Problems in Context

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.
Which inequality represents the situation?

• x + y ≤ 8
• x + y ≤ 6
• 2x + 3y ≤ 6
• x + y ≤ 10

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

• 2x + 3y ≤ 18
• x + y ≤ 6
• x + y ≤ 9
• 3x + 2y ≤ 18

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Sarah makes $30 for each small purse (x) and $50 for each big purse (y). What is the objective quantity?

• P = 30x + 50y
• P = 50x + 30y

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.SSE.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.2

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped.  The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg. What are the variables you need to define?

• x is gas, y is mileage
• x is car, y is moped
• x is gas, y is moped
• x is car, y is mileage

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

Write the system of inequalities
Carlos works at a movie theater selling tickets. The theater has 300 seats and charges $7.50 for adults and $5.50 for children. The theater expects to make at least $2000 for each showing.  

• x+y≤300
  7.5x+5.5y≥2000
• x+y<300
  7.5x+5.5y≥2000
• x+y≤300
  7.5x+5.5y≤2000
• x+y>2000
  7.5x+5.5y≤300

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.CED.A.3

CCSS.HSA.REI.D.12

Lexie is making apple cobblers and apple pies for a bake sale. A cobbler needs 6 cups of apples and a pie needs 2 cups of apples. She also needs to use 4 cups of flour for a cobbler and 2 cups of flour for a pie. Lexie has 18 cups of apples and 16 cups of flour.

x= # of cobblers and y is # of pies

write the inequality for the amount of apples

Lexie is making apple cobblers and apple pies for a bake sale. A cobbler needs 6 cups of apples and a pie needs 2 cups of apples. She also needs to use 4 cups of flour for a cobbler and 2 cups of flour for a pie. Lexie has 18 cups of apples and 16 cups of flour.

x= # of cobblers and y is # of pies

write the inequality for the amount of flour

Lexie is making apple cobblers and apple pies for a bake sale.

.

x= # of cobblers and y is # of pies

She makes $6 profit for each cobbler and $5 profit for each pie.

Select an objective function that models the total profit from cobblers and pies.

Which system of inequalities matches the graph?

• y > 2x - 4
  y < 2
• y < 2x - 4
  y < 2
• y > 2x - 4
  y <  2 
• y < 2x - 4
  y <   -2

Tags

CCSS.HSA.REI.D.12

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.

Define the variables.

• x = eggs

  y = profit

• x = chocolate cake

  y = sponge cake

• x = sponge cake

  y = chocolate cake

• x = profit

  y = eggs