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For which inequality is (0, 9) a possible solution?

For which inequality is (–5, 1) a possible solution?

For which inequality is (–50, –50) a possible solution?

What is the boundary line for the linear inequality y – 2x 10?

Which test point is in the solution set for the linear inequality
{(x, y) | 5x – 2y 10, x R, y R}?

Which test point is in the solution set for the linear inequality
{(x, y) | 7x + 5y 0, x I, y I}?

How would you graph the solution set for the linear inequality 4y – 2x < 20?

What system of linear inequalities is shown here?

Describe the boundary lines for the following system of linear inequalities.
{y 2 + x, x + y 0, x R, y   R}

Which test point is in the solution set for the following system of linear inequalities?
{10y – 5x 0, 4x + 2y > 10, x   I, y I}

What system of linear inequalities is shown here?

A vending machine sells juice and pop.
• The machine holds, at most, 200 cans of drinks.
• Sales from the vending machine show that at least 3 cans of juice are sold for each can of pop.
• Each can of juice sells for $1.50, and each can of pop sells for $1.00.
Let x represent the number of cans of pop.
Let y represent the number of cans of juice.
How would you write the objective function for revenue, R?

Jan volunteers to fold origami frogs and swans for a display.
• She has 8 squares of green paper for the frogs and 12 squares of white paper for the swans.
• It takes her 4 min to fold an origami frog and 3 min to fold an origami swan.
• There must be two swans for every frog.
Let f represent the number of frogs.
Let s represent the number of swans.
Which of the following points is in the feasible region?

Which location best describes where would you find the optimal solutions to an objective function?

The following model represents an optimization problem. Determine the maximum solution.
Restrictions:
x R
y R

Constraints:
x 4
x – y 12
x + 3y 24

Objective function:
G = x – 2y

Graph the solution set for the linear inequality 5y – 2x 15.

The following model represents an optimization problem. Determine the maximum solution.
Restrictions:
x R
y R

Constraints:
x 0
y 0
2x + y 10
x + y 20

Objective function:
Q = 2y – 10x

A butcher shop makes hamburger patties and sausages. Hamburger patties sell for $2.50 and sausage sell for $2. The butcher noticed that they always sell at least four times as many hamburger patties as sausages. The butcher never sells more than 1000 hamburger patties.
Let h represent the number of hamburger patties sold.
Let s represent the number of sausages sold.
Write a system of linear inequalities to describe the constraints. Then, write an objective function that represents the profit made from the sale of hamburger patties and sausages.

For every quilt that is sold at a fundraising banquet, $90 goes to charity. For every ticket that is sold, $65 goes to charity. The organizers’ goal is to raise at least $7000. The organizers need to know how many quilts and tickets must be sold to meet their goal.
a) Define the variables and write a linear inequality to represent the situation.
b) Graph the linear inequality to help you determine whether each of the following points is in the solution set. The first coordinate is the number of quilts and the second is the number of tickets.
i) (40, 50)      ii) (10, 100)      iii) (20, 75)

The staff in a cafeteria are making two kinds of sandwiches: salami and cheese.
• A maximum of 820 sandwiches are needed.
• Based on previous demand, there should be at least two cheese sandwiches for every three salami sandwiches.
a) Define the variables and write a system of inequalities that models this situation.
b) Suggest two combinations of numbers of sandwiches that the cafeteria staff could make.

Andrew has two summer jobs.
• He works no more than a total of 25 h a week. Both jobs allow him to have flexible hours but in whole hours only.
• At one job, Andrew works no less than 12 h and earns $9.00/h.
• At the other job, Andrew works no more than 20 h and earns $8.25/h.
What combination of numbers of hours will allow him to maximize his earnings? What can he expect to earn?