Name: ______________________
Class: _________________
Date: _________
ID: A
Algebra 2 Unit 1 Review (Linear Programming)
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Your computer supply store sells two types of inkjet printers. The first, type A, costs $245 and you
make a $26 profit on each one. The second, type B, costs $152 and you make a $12 profit on each one.
You can order no more than 140 printers this month, and you need to make at least $2660 profit on
them. If you must order at least one of each type of printer, how many of each type of printer should
you order if you want to minimize your cost?
a.
b.
____
of
of
of
of
type
type
type
type
A
B
A
B
c.
d.
70
70
60
80
of
of
of
of
type
type
type
type
A
B
A
B
2. Your furniture store sells two types of dining room tables. The first, type A, costs $202 and you make a
$22 profit on each one. The second, type B, costs $179 and you make a $12 profit on each one. You
can order no more than 120 tables this month, and you need to make at least $1640 profit on them. If
you must order at least one of each type of table, how many of each type of table should you order if you
want to minimize your cost?
a.
b.
____
80
60
70
70
37 of type A
83 of type B
20 of type A
100 of type B
c.
d.
100 of type A
20 of type B
83 of type A
37 of type B
3. Your Surf Shop sells two types of surfboards. The first, type A, costs $248 and you make a $22 profit on
each one. The second, type B, costs $101 and you make a $18 profit on each one. You can order no
more than 150 surfboards this month, and you need to make at least $2940 profit on them. If you must
order at least one of each type of surfboard, how many of each type of surfboard should you order if you
want to minimize your cost?
a.
b.
78
72
72
78
of
of
of
of
type
type
type
type
A
B
A
B
c.
d.
1
60
90
90
60
of
of
of
of
type
type
type
type
A
B
A
B
Name: ______________________
ID: A
Solve the system of inequalities by graphing.
____
4. y ≥ −3x − 2
y ≤
1
4
x−1
a.
c.
b.
d.
2
Name: ______________________
____
ID: A
5. y ≤ −2x − 2
y > 2x − 2
a.
c.
b.
d.
Short Answer
6. Your club is baking vanilla and chocolate cakes for a bake sale. They need at most 26 cakes. You cannot
have more than 10 chocolate cakes. Write and graph a system of inequalities to model this system.
7. An exam consists of two parts, Section X and Section Y. There can be a maximum of 90 questions. There
must be at least 10 more questions in Section Y than in Section X. Write a system of inequalities to model
the number of questions in each of the two sections. Then solve the system by graphing.
8. An after-school program consists of two groups, Section X and Section Y. In order for the program to
run, there must be at least 85 students total. There must be at most 20 less students in Section Y than in
Section X. Write a system of inequalities to model the number of students in each of the two sections.
Then solve the system by graphing.
3
Name: ______________________
ID: A
Graph the system of constraints and find the value of x and y that maximize the objective
function.
9. Constraints
x ≥ 0
y ≥ 0
y ≤
1
3
x+1
5 ≤ y+x
Objective function: C = 6x − 4y
10. Constraints
x ≥ 0
y ≥ 0
y ≤ 3
y < − 2x + 5
Objective function: C = −9x + 2y
What point in the feasible region maximizes the objective function?
11. Constraints
x ≥ 0
y ≥ 0
−x + 5 ≤ y
y ≤
1
3
x+3
Objective function: C = 5x − 2y
12. Constraints
x ≥ 0
y ≥ 0
y ≤ 3
y < − 2x + 5
Objective function: C = −8x + y
4
Name: ______________________
13. Constraints
ID: A
x ≥ 0
y ≥ 0
y ≤ 3
y < −x+5
Objective function: C = −6x + 5y
Given the system of constraints, name all vertices. Then find the maximum value of the
given objective.
14. x ≥ 0
y ≥ 0
y ≤
1
3
x+2
4 ≤ y+x
Objective function: C = 4x − 2y
15. Find the values of x and y that maximize the objective function P = 3x + 2y for the graph. What is the
maximum value?
16. A factory can produce two products, x and y, with a profit approximated by P = 13x + 24y − 1000. The
production of y can exceed x by no more than 100 units. Moreover, production levels are limited by the
formula x + 2y ≤ 2900 What production levels yield maximum profit?
5
Name: ______________________
ID: A
17. A company can produce two products, x and y, with a profit approximated by P = 14x + 21y − 800. The
production of y can exceed x by no more than 100 units. Moreover, production levels are limited by the
formula x + 2y ≤ 500 What production levels yield maximum profit?
18. A car manufacturing company produces two models of cars, A and B. The profit on car A is $2000 per
car and on car B is $3000 per car. The company can produce a maximum of 3000 cars of type A and
2000 cars of type B per year. If the company can produce a maximum of 15,000 cars per year, write a
system of inequalities required to find the maximum profit.
19. A garment company makes two types of woolen sweaters and can produce a maximum of 700 sweaters
per week. Each sweater of the first type requires 2 pounds of green wool and 4 pounds of pink wool to
produce a single sweater. The second type of sweater requires 4 pounds of green wool and 3 pounds of
pink wool. The profit earned on the first type of sweater is $5 and on the second type is $7. If the
company has 50 pounds of green wool and 80 pounds of pink wool, write a system of inequalities to
represent the possible number of sweaters of each type that can be made per week. Draw a graph showing
the feasible region and list the coordinates of the vertices of the feasible region. Also, find the maximum
profit.
Essay
20. A garment manufacturing company produces two types of shirts: formal and casual. The company can
produce a maximum of 700 shirts in a day. If all the shirts are casual, the company can produce a total of
300 shirts in a day. The company makes a profit of $5 on each casual shirt and a profit of $6 on each
formal shirt. Use the information about the shirts to explain how linear programming can be used to
calculate maximum profit. Include the system of inequalities that represents the constraints that are used
to maximize the profit that depends on the number of shirts produced in a day.
6