Solving/interpreting linear inequalities in two variables

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.

Select the TWO(2) invisible constraints.

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

Your class is taking a trip to a nature preserve in small and/or large vans. A small van holds 8 people, and a large van holds 12 people. Forty-eight people will be taking the trip.

Which of the following are not possible combinations of vans that could be used?

• (6,0)

• (0,4)

• (3,2)

• (4,4)

• The cost of 1 sundae is $4.00

• The cost of 1 ice-cream cone is $2.50

• The total cost of 1 ice-cream cone and 1 sundae is $5.00

• The total cost of 1 ice-cream cone and 1 sundae is $8.00

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.

Write the Objective Function.

• P = 5x + 7y

• P = 7x + 3y

• P = 6x + 3y

• P = 70x + 70y

Objective function:

P = 30x + 50y

The vertex that maximizes profit is (0, 6). What is the profit?

• $300

• $280

• $400

• $240

Martha is buying plants and soil for her garden. The soil (x) costs $4 per bag, and the plants (y) cost $10 each. She wants to buy at least 5 plants and spend no more than $100. Write a system of linear inequalities to model the situation.

• x = 3 and y = 8

• y ≤ 5 and 10 + 4 ≥ 100

• x ≥ 0 and x + y ≤ 100

• 10x + 4y ≤ 100 and x ≥ 5

You can work at most 20 hours next week. You need to earn at least $92 to cover you weekly expenses. Your math tutoring job pays $7.50 per hour and your job as a pet sitter pays $6 per hour. You can work at most 7 hours tutoring. Which system of linear inequalities to models the situation?

• s + t < 20

  
  

  6s + 7.50t ≥ 92

  
  

  t >7

• s + t ≤ 20

  
  

  6s + 7.50t ≥ 92

  
  

  t ≤ 7

Luka and Dana are making cookies for the Westland Pantry. They only have up to 8 hours to bake! They can bake 32 chocolate chip cookies in an hour (x), and 20 snickerdoodle cookies in an hour (y). They need to make at least 150 cookies. Which region represents less than 8 hours baking and over 150 cookies made?

• Red

• Blue

• Purple (overlap of red and blue)

• Non- Shaded

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

• 30x + 50y
• 50x + 30y