Linear Programming Test Review

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

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

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) constraints restricting the number of cakes made.

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 constraint needed for number of eggs used.

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.

Graph the 5 constraints and select number that represents the feasible region.

• 1

• 2

• 3

• 4

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 FOUR(4) critical (corner) points of the feasible region.

 

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 chocolate cakes does Chef Ben need to sell to maximize profits?

• 0

• 10

• 7

• 30

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

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.

What is the maximum profit Chef Ben makes?

• $67.80

• $57

• $51

• $30