Name: 

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

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

What is the boundary line for the linear inequality 3x – 6y < 18?

Which test point is in the solution set for the linear inequality
{(x, y) | x + y < 3, x W, y W}?

What system of linear inequalities is shown here?

Which system of linear inequalities has no solution?

A football stadium has 60 000 seats.
• 70% of the seats are in the lower deck.
• 30% of the seats are in the upper deck.
• At least 40 000 tickets are sold per game.
• A lower deck ticket costs $100, and an upper deck ticket costs $60.
Let x represent the number of lower deck tickets.
Let y represent the number of upper deck tickets.
What are the restrictions on x and y?

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.
How would you write the objective function for time, T?

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.
Which of the following is a constraint of this optimization problem?

Where might you find the maximum solution to the objective function?
Restrictions:
x   R
y R

Constraints:
–2 x 4
–2 y 4

Objective function:
B = 2y + 3x

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

Constraints:
y 0
x y + 10
2x + y 80

Objective function:
T = 2y – x

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

Constraints:
x > 0
y < 10
x – y 6

Objective function:
P = 10x + 2y

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

Audrey notices the number of people and dogs in a dog park.
• There are more people than dogs.
• There are at least 12 dogs.
• There are no more than 40 people and dogs, in total.
Let d represent the number of dogs and let p represent the number of people.
Which inequality represents a restriction of d and p based on the given information?

Audrey notices the number of people and dogs in a dog park.
• There are more people than dogs.
• There are at least 12 dogs.
• There are no more than 40 people and dogs, in total.
Let d represent the number of dogs and let p represent the number of people.
Which inequality represents a restriction of d and p based on the given information?

Graph the solution set for the following system of inequalities.
{(x, y) | x + 2y 2, y + 2 > x, x R, y R}

Graph the solution set for the following system of inequalities.
{(x, y) | x + y > 0, x + y < 4, x R, y R}

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

The staff in a cafeteria are making two kinds of sandwiches: submarines and cream cheese bagels.
• A maximum of 570 sandwiches are needed.
• Based on previous demand, there should be at least five submarine sandwiches for every three cream cheese bagels.
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.

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.

On a flight between Calgary and Thunder Bay, there are business class and economy seats.
• At capacity, the airplane can hold no more than 133 passengers.
• No fewer than 124 economy seats are sold, and no more than 5 business class seats are sold.
• The airline charges $624 for business class seats and $239 for economy seats.
What combination of business class and economy seats will result in the maximum revenue? What will this maximum revenue be?