Linear Programming Practice

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

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A2.ACE.3

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 cake 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.​

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A2.ACE.3

Given the objective function: P = 30x + 50y

Which vertex maximizes the profit?

• (0,0)

• (6,2)

• (8,0)

• (0,6)

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A2.ACE.3

• (0, 6), (0, 20), (10, 10), (14, 6) and (10, 6

• (0, 20), (10, 10), and (10, 6)

• (0, 6), (10, 10), and (10, 6)

• (0, 6), (0, 20), (10, 10), and (10, 6)

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A2.ACE.3

What do you call the area where all the shading overlaps?

• the answer

• the feasible region

• the void

• the objective function

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A2.ACE.3

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. She will make $4000 profit per acre of soybeans and $3000 per acre of corn. If x represents acres of soybeans and y represents acres of corns, which inequalities represent the constraints to her situation?

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A2.ACE.3

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. She will make $4000 profit per acre of soybeans and $3000 per acre of corn. If x represents acres of soybeans and y represents acres of corns, which expression represents the objective function to her situation?

• min 4000x + 3000y

• max 4000x + 3000y

• 4000x + 3000y > 21000

• max 3000x + 4000y

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A2.ACE.3

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. She will make $4000 profit per acre of soybeans and $3000 per acre of corn. If x represents acres of soybeans and y represents acres of corns. What are the critical points for her situation?

• (0, 6), (3, 3) and (7.5, 0)

• (0, 5) and (3, 3)

• (0, 5), (3,3) and (6, 0)

• (3, 3) and (6, 0)

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A2.ACE.3

• x = 0, y = 300

• x = 150, y = 150

• x = 100, y = 150

• x = 150, y = 100

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A2.ACE.3

A doctor wishes to mix two types of foods in such a way that the vitamin contents of the mixture contain at least 8 units of vitamin A and 10 units of vitamin C. Food ‘x’ contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Food ‘y’ contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs $50 per kg to purchase Food ‘x’ and $70 per kg to purchase Food ‘y’. Formulate this problem as a linear programming problem to minimize the cost of such a mixture.

Which objective function and constraints fit this scenario?

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A2.ACE.3