Chapter 7 Practice Test
Complete all work on your own paper.
1. Graph the solution to this system of linear inequalities
𝑦 ≥ −𝑥 + 3
1
{𝑦 ≤ 𝑥 − 2
4
𝑥<8
Note: The line x = 8 should be dotted. The software I am using does not allow for that option.
2. Graph the solution to this system of linear inequalities.
𝑦 < −2𝑥
{ 𝑦 ≤ 4𝑥
𝑦 ≥ −𝑥 − 5

y

















x




















3. Identify three points that are solutions to each system.
There are infinite points to these systems. Find where they are shaded and choose three points
from the shaded regions.
a. {
𝑦 ≥ −𝑥 + 3
𝑦 > 3𝑥 + 1
b. {
𝑦 < 6𝑥 − 5
𝑦 ≥ −2𝑥
4. A company prints flyers and brochures. It takes 2 minutes to print a flyer and 4 minutes to print a
brochure. Each flyer uses 12 ounces of ink and each brochure uses 9 ounces of ink. The company has 2
hours available and 360 ounces of ink. The company makes a profit of $1 on each flyer and $2 on each
brochure. The company cannot print a negative number of flyers or brochures.
a. Let x represent the number of flyers and y represent the number of brochures. Write and graph
the system of inequalities to represent the constraints of this problem situation.
2𝑥 + 4𝑦 ≤ 120
12𝑥 + 9𝑦 ≤ 360
𝑥≥0
𝑦≥0
The vertices are: (0,0), (0, 30), (30,0), (12, 24)
b. How many fliers and brochures should the company produce to maximize their profit?
Use the equation 𝑝(𝑥, 𝑦) = 1𝑥 + 2𝑦 on the vertices above.
You’ll maximize your profit when produce:
 0 fliers and 30 brochures or
 12 fliers and 24 brochures
5. Write a system of linear inequalities that is represented by the graph.
𝑦 ≤𝑥+4
𝑦≥𝑥
𝑥 > −3
𝑦≤1
6. A farmer grows corn and tomatoes. There is an expected demand of at least 2000 ears of corn and 3500
tomatoes each week. A total of more than 6000 food items must be grown each week. The farmer also
wants to grow at least twice as many tomatoes as ears of corn. Write a system of linear inequalities to
represent the constraints of this situation. Let c represent the number of ears of corn and t represent the
number of tomatoes.
2000𝑐 + 3500𝑡 ≥ 6000
𝟐𝒄 < 𝒕
7. Wanda sews small and large gloves. It takes her 45 minutes to sew a small pair of gloves and 120
minutes to sew a large pair of gloves. The costs of producing the gloves are $2 for a small pair and $4
for a large pair. Wanda has 16 hours available to sew gloves. The materials to make the gloves must cost
at most $40. The system of linear inequalities represents this situation.
45𝑥 + 120𝑦 ≤ 960
{
2𝑥 + 4𝑦 ≤ 40
What does the solution (16, 2) represent?
The point (16, 2) is a vertex for the region bounded by the inequalities. In particular, it represents the
point at which the cost or the profit is either maximized or minimized. For our purposes, we may say
that it represents the production of 16 large gloves and 2 small gloves.
8. A company manufactures lunchboxes using two machines. Machine A takes 2 minutes to make one
lunchbox and Machine B takes 3 minutes to make one lunchbox. The costs of producing the lunchboxes
are $5 using Machine A and $6 using Machine B. The company can expense 60 hours of labor each
week. The resources to make the lunchboxes must be at most $8,400 each week. The system of linear
inequalities represents this situation.
2𝑥 + 3𝑦 ≤ 3600
{
5𝑥 + 6𝑦 ≤ 8400
What does the solution (1200, 400) represent?
The point (1200, 400) is a vertex for the region bounded by the inequalities. In particular, it represents
the point at which the cost or the profit is either maximized or minimized. For our purposes, we may
say that it represents the production of 1200 lunchboxes from machine A and 400 lunchboxes from
machine B .
9. A baker is baking cookies and brownies. It takes 12 minutes to bake a batch of cookies and 20 minutes
to bake a batch of brownies. Each batch of cookies uses 1 cup of flour and each batch of brownies uses 5
cups of flour. The baker has 10 hours available and 100 cups of flour. The baker makes a profit of $8 on
each batch of cookies and $10 on each batch of brownies. How many batches of cookies and brownies
should the baker make in order to maximize profit? (You must show your work.)
a.
b.
c.
d.
0 batches of cookies and 0 batches of brownies
0 batches of cookies and 20 batches of brownies
50 batches of cookies and 0 batches of brownies
25 batches of cookies and 15 batches of brownies