What does this linear programming worksheet cover?

This worksheet teaches students to model optimization situations by defining decision variables, writing profit objective functions, and selecting the correct resource constraints. Its 11 multiple-choice and 2 multiple-select items use production and farming word problems to require students to match product quantities, profit coefficients, resource-use coefficients, and available limits.

How can I use this worksheet to teach linear programming modeling?

Have students first underline the products, profits, and available resources in each scenario, then define x and y before attempting the answer choices. Use the purse-and-shoe, candy, or soccer-ball problems to build a class table of resource use, objective-function coefficients, and right-hand limits; then ask students to explain why a machine-hours inequality differs from a labor-hours inequality.

What mistakes should I watch for when students complete this worksheet?

Watch for students defining variables as profits or hours instead of as the quantities of the two products, such as purses and pairs of shoes. Students may also place resource-use numbers in the objective function, swap coefficients between products, match a limit to the wrong resource, or select only one of the two constraints in a multiple-select item. Because the scenarios describe maximum available resources, students should also check the inequality direction and include nonnegative variable conditions when the question requires the full constraint model.

How do I assign and grade this linear programming worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for the 13 variable, objective-function, and constraint items. Assign the PDF for written modeling practice or use the digital version for automatic response collection; printable submissions can also be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing and font size so the algebraic expressions and multi-step production scenarios are easier to read. You can also apply a dyslexia-friendly font or translate the word-problem prompts into another language while students work on identifying variables, objective functions, and resource inequalities.

Where can I find more worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, including downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

Linear Programming Practice - Algebra 2 - Free Printable Worksheet

1.

A factory makes purses and shoes. For each purses, you make a $100 profit. For each pair of shoes, you make $50 profit. A purse takes 3 machine hours and 5 man hours. A pair of shoes requires 4 machine hours and 2 man hours. The machine can operate for up to 50 hours. The total number of man hours is 60. How many purses and pairs of shoes should the factory make in order to maximize profits?

What are the variables for this situation

a)

X = profit

Y = cost

b)

X = machine hours

Y = man hours

c)

X = purses

Y = pairs of shoes

d)

X = man hours

Y = Profits

2.

A factory makes purses and shoes. For each purses, you make a $100 profit. For each pair of shoes, you make $50 profit. A purse takes 3 machine hours and 5 man hours. A pair of shoes requires 4 machine hours and 2 man hours. The machine can operate for up to 50 hours. The total number of man hours is 60. How many purses and pairs of shoes should the factory make in order to maximize profits?

Given that X = # of Purses and that Y = # of pairs of shoes

What is the objective function?

a)

P = 4x + 3y

b)

P = 100X + 50y

c)

P = 3x + 5y

d)

P = 4x + 2y

3.

A factory makes purses and shoes. For each purses, you make a $100 profit. For each pair of shoes, you make $50 profit. A purse takes 3 machine hours and 5 man hours. A pair of shoes requires 4 machine hours and 2 man hours. The machine can operate for up to 50 hours. The total number of man hours is 60. How many purses and pairs of shoes should the factory make in order to maximize profits?

Given that x = # of Purses and y = # of pairs of shoes

What inequality represents the constraint of man hours?

a)

4x + 2y < 50

b)

5x + 2y < 60

c)

3x + 5y < 50

d)

5x + 2y < 50

4.

A factory makes purses and shoes. For each purses, you make a $100 profit. For each pair of shoes, you make $50 profit. A purse takes 3 machine hours and 5 man hours. A pair of shoes requires 4 machine hours and 2 man hours. The machine can operate for up to 50 hours. The total number of man hours is 60. How many purses and pairs of shoes should the factory make in order to maximize profits?

Given that x = # of Purses and y = # of pairs of shoes

What inequality represents the constraint of machine hours?

a)

4x + 3y < 50

b)

3x + 4y < 60

c)

3x + 4y < 50

d)

5x + 2y < 60

5.

The Wily Monka Chocolate Factory makes 2 kinds of candies: Everlasting Goobstoopers and Monka Bars. The profit for a case of Everlasting Goob Stoopers is $20. The profit for a case of Monka Bars is $35. The goobstoopers have to have 4 machine hours and 5 man hours. The Monka bar has to have 5 machine hours and 10 man hours. There are only 410 machine hours and 700 Man hours available. How many cases of each kind of candy should the factory make to maximize profit?

How would you define your varaibles for this problem?

a)

x = Profit

y = cst

b)

x = cases of Everlasting Goobstoopers

Y = cases of Monka Bars

c)

x = candies

y = hours

d)

x = man hours

y = machine hours

6.

The Wily Monka Chocolate Factory makes 2 kinds of candies: Everlasting Goobstoopers and Monka Bars. The profit for a case of Everlasting Goob Stoopers is $20. The profit for a case of Monka Bars is $35. The goobstoopers have to have 4 machine hours and 5 man hours. The Monka bar has to have 5 machine hours and 10 man hours. There are only 410 machine hours and 700 Man hours available. How many cases of each kind of candy should the factory make to maximize profit?

Given that x = cases od Everlastign Goobstoopers and y = cases of Monka Bars

What is the objective function?

a)

P = 20x + 35y

b)

P = 4x + 5y

c)

P = 35x + 20y

d)

P = 5x + 10y

7.

The Wily Monka Chocolate Factory makes 2 kinds of candies: Everlasting Goobstoopers and Monka Bars. The profit for a case of Everlasting Goob Stoopers is $20. The profit for a case of Monka Bars is $35. The goobstoopers have to have 4 machine hours and 5 man hours. The Monka bar has to have 5 machine hours and 10 man hours. There are only 410 machine hours and 700 Man hours available. How many cases of each kind of candy should the factory make to maximize profit?

Given that x = cases od Everlastign Goobstoopers and y = cases of Monka Bars

What are the TWO constraint inequalities?

a)

4x + 5y < 410

b)

4x + 5y < 700

c)

5x + 10y < 410

d)

5x + 10y < 700

8.

A factory makes soccer balls and basketballs. The soccer ball requires 4 hours in the fabrication department and the basketball requires 2 hours in the fabrication department. The soccer ball requires 1 hour in the finishing department and the basketball requires 2 hours in the finishing department. The fabrication department has 100 hours available per day and the finishing department has 40 hour available per day. If the profit on the soccer ball is $8 and the profit on the basketball is $10, how many of each should be produced each day to maximize profit?

Define your variables.

a)

x = fabrication hours

y = finishing hours

b)

x = Profit

y = cost

c)

x = # of workers in the factory

y = the # of hours the factory is open

d)

x = # of soccer balls

y =# of basketballs

9.

A factory makes soccer balls and basketballs. The soccer ball requires 4 hours in the fabrication department and the basketball requires 2 hours in the fabrication department. The soccer ball requires 1 hour in the finishing department and the basketball requires 2 hours in the finishing department. The fabrication department has 100 hours available per day and the finishing department has 40 hour available per day. If the profit on the soccer ball is $8 and the profit on the basketball is $10, how many of each should be produced each day to maximize profit?

Given that x = # of soccer balls and y = # of basketballs

What is the objective function?

a)

P = 10x + 8y

b)

P = 8x + 10y

c)

P = 4x + 2y

d)

P = x + 2y

10.

A factory makes soccer balls and basketballs. The soccer ball requires 4 hours in the fabrication department and the basketball requires 2 hours in the fabrication department. The soccer ball requires 1 hour in the finishing department and the basketball requires 2 hours in the finishing department. The fabrication department has 100 hours available per day and the finishing department has 40 hour available per day. If the profit on the soccer ball is $8 and the profit on the basketball is $10, how many of each should be produced each day to maximize profit?

Given that x = # of soccer balls and y = # of basketballs

What are the TWO inequalities that represent the constraints?

a)

4x + 2y < 40

b)

4x + 2y < 100

c)

x + 2y < 40

d)

x + 2y < 100

11.

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 barley can be modeled by P=4000x+3000y . If x represents acres of soybeans and y represents acres of corns, which inequalities represent the constraints of the problem?

a)

x≥0

y≥0

x+y≥6

3x+2y≥15

b)

x≥0

y≥0

x+y≤6

2x+3y≤15

c)

x≥0

y≥0

4000x+y≤6

2x+600y≤15

d)

P=4000x+3000y

12.

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

a)

$P=2x+3y$

b)

$P=5x+6y$

c)

$P=3x+2y$

d)

$P=3x+5y$

13.

A farmer has a field where he can plant either wheat or barley or a combination of both. Each hectare of wheat requires 3 units of water and 2 units of fertilizer, while each hectare of barley requires 2 units of water and 3 units of fertilizer. If the farmer has 15 units of water and 15 units of fertilizer available, which of the following represents the constraint for the fertilizer?

a)

$2x + 3y \leq 15$

b)

$3x + 2y \leq 15$

c)

$2x + 2y \leq 15$

d)

$3x + 3y \leq 15$

Linear Programming Practice - Algebra 2

Linear Programming Practice - Algebra 2

Total questions: 13

Linear Programming Practice - Algebra 2

Total questions: 13

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