Unit Test #1 Review: Ch. 5 - Linear Inequalities
Name:________________
Multiple Choice: Identify the choice that best completes the statement or answers the question.
____ 1. For which inequality is (–5, 1) a possible solution?
a. y > 9
b. y – 2x 10
c. y –9 + 2x
d. y < x – 2
____ 2. What is the boundary line for the linear inequality 2x + 2y < 16?
a. y = 8 – x
b. x = 8 – y
c. y = 16 – x
d. y = 4 – 2x
____ 3. Identify the point of intersection for the following system of linear inequalities.
{2y – 6x < 12, 4x + 4y 8, x I, y I}
a. (–3, 1)
b. (–1, 3)
c. (3, –1)
d. (1, –3)
____ 4. What system of linear inequalities is shown here?
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
a. 2x + y  1
y > 2x – 3
b. 2x + y 1
y 2x – 3
c. 2x + y > 1
y > 2x – 3
d. 2x + y > 1
y 2x – 3
–2
–3
–4
–5
____ 5. How would you graph the solution set for the linear inequality y + 5x 2?
a. Draw a dashed boundary line y = –5x + 2, then shade above the line.
b. Draw a solid boundary line y = –5x + 2, then shade above the line.
c. Draw a solid boundary line y = –5x + 2, then shade below the line.
d. Draw a dashed boundary line y = –5x + 2, then shade below the line.
____ 6. What is the boundary line for the linear inequality y – 2x 10?
a. y = –2x – 10
b. y = 2x + 10
c. y = 2x – 10
d. y = –2x + 10
____ 7. Which test point is in the solution set for the linear inequality
{(x, y) | 7x – 5y < 0, x R, y R}?
a. (1, –1)
b. (-2, 5)
c. (2,2)
d. (0, 0)
____ 8.
Which test point is in the solution set for the linear inequality
{(x, y) | 5x – 2y 10, x R, y R}?
a. (5,2)
b. (2,5)
c. (1,0)
d. (0,1)
____ 9. What system of linear inequalities is shown here?
y
a. 2x + 3y  6
5
y > 2x – 3
4
3
b. 2x + 3y < 6
2
y > 2x – 3
1
c. 2x + 3y < 6
y 2x – 3
x
–5 –4 –3 –2 –1
1
2
3
4
5
–1
d. 2x + 3y ≥ 6
–2
y 2x – 3
–3
–4
–5
____10. What system of linear inequalities is shown here?
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
a. 3x + y ≤ 0
y + 4 ≥ -3x
b. 3x + y < 0
y + 4 3x
c. 3x + y < 0
y – 4 > 3x
d. 3x + y > 0
y + 4 3x
–4
–5
____11. What system of linear inequalities is shown here?
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
a. 2x + y 4
y < 2x – 3
b. 2x + y 4
y > 2x – 3
c. 2x + y 4
y > 2x – 3
d. 2x + y 4
y < 2x – 3
____ 12. 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.
What are the restrictions on x and y?
a. x  W, y  W
b. x  I, y  I
c. x  R, y  R
d. No constraints.
Short Answer
13. Graph the solution set for the linear inequality 5y – 2x 15.
14. What system of linear inequalities
15. What system of linear inequalities is shown
is shown here?
here?
y
–5
–4
–3
–2
y
5
5
4
4
3
3
2
2
1
1
–1
–1
1
2
3
4
5
x
–5
–4
–3
–2
–1
–1
–2
–2
–3
–3
–4
–4
–5
–5
1
2
3
4
5
16. Which side of the boundary line is the solution set for the linear inequality
x + 2y – 1 > 0?
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
x
17. Complete the graph of the solution set for the following system of inequalities.
{(x, y) | y 3x, 2x + 3y –3, 𝑥 ∈ 𝑅, 𝑦 ∈ 𝑅}
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
18. A butcher shop makes hamburger patties and sausages. Hamburger patties sell for $2
and sausage sell for $1.50. The butcher noticed that they always sell at least twice as
many sausages as hamburger patties, but never more than 100 hamburger patties or 300
sausages.
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.
19. April notices the number of people and dogs in a dog park.
• There are more than twice as many people as dogs.
• There are at least 10 dogs.
• There are no more than 50 people and dogs, in total.
Write a system of linear inequalities to describe the constraints. Graph the system. What
are the maximum and minimum number of legs at the dog park?
20. A fast-food concession stand sells hot dogs and hamburgers.
• Daily sales can be as high as 250 hamburgers and hot dogs combined.
• The stand has room to stock no more than 200 hot dogs and no more than 120
hamburgers.
• Hot dogs are sold for $3, and hamburgers are sold for $5.
Create a model that could be used to determine the combination of hamburgers and hot
dogs that will result in maximum sales.
Unit Test #1 Review: Ch. 5 - Linear Inequalities
Answer Section: MULTIPLE CHOICE
1. ANS: B
7. ANS: B
8. ANS: A
2. ANS: A
9. ANS: A
3. ANS: B
10.
ANS:
A
11.
ANS:
B
12.
ANS:
A
4. ANS: C
5. ANS: C
6. ANS: B
SHORT ANSWER
13. ANS:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
–2
–3
–4
–5
14. ANS:
{(x, y) | x + 4y > 4, y
5x – 5, x
R, y
15. ANS:
{(x, y) | x
2.5, y > -3, x
16. ANS:
Above the line
R, y
R}
R}
5
x
17. ANS:
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
18. ANS:
Constraints:
h 0
s 0
h 100
s 300
2h s
Objective function:
P = 2h + 1.5s
1
2
3
4
5
x
19. ANS:
Maximum: 132 legs
Minimum: 80 legs
20. ANS:
Let x represent the number of hamburgers.
Let y represent the number of hot dogs.
Let R represent the sales revenue.
x  W, y  W
x 120
y 200
x + y 250
Objective function to maximize:
R = 5x + 3y
Graph the line x = 120 and shade the region between it and the y-axis.
Graph the line y = 200 and shade the region between it and the x-axis.
Graph the line x + y = 250 and shade the region below it and bounded by the axes. The feasible region
is all the whole number points in the overlapping area and its boundaries.
200
y
180
160
140
120
100
80
60
40
20
20
40
60
80 100 120 140 160 180
x