Linear Programming Application Practice

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with corn can be modeled by P=4000x+3000y .  If x represents acres of soybeans and y represents acres of corns, which inequalities represent the possible solutions to her situation?

• x≥0
  y≥0
  x+y≥6 
  3x+2y≥15
• x≥0 
  y≥0 
  x+y≤6
  2x+3y≤15
• x≥0 
  y≥0 
  4000x+y≤6
  2x+600y≤15
• P=4000x+3000y

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with corn can be modeled by P=4000x+3000y . What is the maximum profit that she can earn?

• $15,000
• $21,000
• $18,000
• $24,000

A farmer can plant up to 6 acres of land with soybeans and corn. Her use of a necessary pesticide is limited by federal regulations to 15 gallons for her entire 6 acres. Soybeans require 2 gallons of pesticide for every acre planted and corn requires 3 gallons per acre. The profit the farmer makes by earning $4,000 for every acre of soybeans she plants and $3,000 for every acre she plants with corn can be modeled by P=4000x+3000y . What combination of soybeans and corn will maximize profit?

• 4 acres of soybeans and 2 acres of corn
• 6 acres of soybeans and 0 acres of corn
• 3 acres of soybeans and 3 acres of corn
• 0 acres of soybeans and 5 acres of corn

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. Between chocolate cakes and sponge cakes, there is only enough time to make 12 cakes total. 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. Between chocolate cakes and sponge cakes, there is only enough time to make 12 cakes total. 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. Between chocolate cakes and sponge cakes, there is only enough time to make 12 cakes total. 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. Between chocolate cakes and sponge cakes, there is only enough time to make 12 cakes total. 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 cakes there is time to make.

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. Between chocolate cakes and sponge cakes, there is only enough time to make 12 cakes total. 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. Between chocolate cakes and sponge cakes, there is only enough time to make 12 cakes total. 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.

List the vertices 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. Between chocolate cakes and sponge cakes, there is only enough time to make 12 cakes total. 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

• $70

• $51

• $30