Chapter 3 Test
Short Answer
1. Graph the system of constraints. Then find the values of x and y that maximize
.
Solve the equation.
2.
Write in standard form an equation of the line passing through the given point with the given slope.
3. slope = –8; (–2, –2)
4. Find the point-slope form of the equation of the line passing through the points (–6, –4) and (2, –5).
Find the slope of the line.
5.
y
4
2
–4
–2
O
2
–2
–4
Solve the system by graphing.
4
x
6.
y
4
2
–4
–2
O
2
4
x
–2
–4
7.
y
4
2
–4
–2
O
2
4
x
–2
–4
Without graphing, classify each system as independent, dependent, or inconsistent.
8.
9.
10.
Solve the system of inequalities by graphing.
11.
y
4
2
–4
O
–2
2
4
x
–2
–4
12.
y
4
2
–4
–2
O
2
4
x
–2
–4
13.
Solve the system by the method of substitution.
14.
15.
16.
17.
18. Given the system of constraints, name all vertices. Then find the maximum value of the given objective function.
Maximum for
y
4
2
–4
–2
O
2
4
x
–2
–4
Essay
19. You are selling cases of mixed nuts and roasted peanuts. Mixed nuts come in 12 cans per case and Roasted Peanuts
come in 20 Packaged per case. Mixed nuts cost $24 per case and Roasted Peanuts cost $15 per case. You can make
$18 profit per case of mixed nuts and $15 profit per case of roasted peanuts. You can order no more than a total of
500 cans and packages and spend no more than $600. How can you maximize your profit? How much is the
maximum profit?
a. Write an system of constraints and an objective function P for a linear program to model
the problem.
b. Graph the constraint and find the coordinates of each vertex.
c. Evaluate P at each vertex to find the maximum profit.
20. You are going to make and sell bread. A loaf of Irish soda bread is made with 4c flour and
c sugar. Kugelhopf
cake is made with 4c flour and 1c sugar. You will make a profit of $.75 on each loaf of Irish soda bread and a
profit of $2.50 on each Kugelhopf cake. Your have 16 c flour and 3 c surgar.
a. Write an system of constraints and an objective function P for a linear program to model
the problem.
b. Graph the constraint and find the coordinates of each vertex.
c. Evaluate P at each vertex to find the maximum profit. How many of each kind of bread
should you make to maximize the profit?
Chapter 3 Test
Answer Section
SHORT ANSWER
1. ANS:
10 y
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8 9
x
Vertices
(0, 0):
(0, 2):
(3, 0):
(3, 5):
When x = 3 and y = 5, P has its maximum value of 270.
PTS: 1
DIF: L2
REF: 3-4 Linear Programming
OBJ: 3-4.1 Finding Maximum and Minimum Values
STA: CA A2 2.0
TOP: 3-4 Example 1
KEY: linear programming | maximum value | maximize
2. ANS:
2
x = 0 or x = 2
3
PTS: 1
DIF: L2
OBJ: 1-5.1 Absolute Value Equations
KEY: absolute value
3. ANS:
8x + y = –18
REF: 1-5 Absolute Value Equations and Inequalities
STA: CA A2 1.0
TOP: 1-5 Example 2
PTS: 1
DIF: L2
REF: 2-2 Linear Equations
OBJ: 2-2.2 Writing Equations of Lines
TOP: 2-2 Example 4
KEY: point-slope form | standard form of linear equation
4. ANS:
1
y + 4 =  (x + 6)
8
PTS: 1
DIF: L2
REF: 2-2 Linear Equations
OBJ: 2-2.2 Writing Equations of Lines
KEY: point-slope form | ordered pair
5. ANS:
0
TOP: 2-2 Example 5
PTS: 1
DIF: L2
OBJ: 2-2.2 Writing Equations of Lines
KEY: slope | equation of a line
6. ANS:
REF: 2-2 Linear Equations
TOP: 2-2 Example 7
y
4
2
–4
–2
O
2
4
x
–2
–4
(3, 1)
PTS: 1
DIF: L2
REF: 3-1 Graphing Systems of Equations
OBJ: 3-1.1 Systems of Linear Equations STA: CA A2 2.0
TOP: 3-1 Example 1
KEY: system of linear equations | graphing
7. ANS:
y
4
2
–4
–2
O
2
4
x
–2
–4
no solutions
PTS: 1
DIF: L2
REF: 3-1 Graphing Systems of Equations
OBJ: 3-1.1 Systems of Linear Equations STA: CA A2 2.0
TOP: 3-1 Example 3
KEY: system of linear equations | graphing | inconsistent system
8. ANS:
inconsistent
PTS: 1
DIF: L2
REF: 3-1 Graphing Systems of Equations
OBJ: 3-1.1 Systems of Linear Equations STA: CA A2 2.0
TOP: 3-1 Example 3
KEY: system of linear equations | inconsistent system
9. ANS:
independent
PTS: 1
DIF: L2
REF: 3-1 Graphing Systems of Equations
OBJ: 3-1.1 Systems of Linear Equations STA: CA A2 2.0
TOP: 3-1 Example 3
KEY: system of linear equations | independent system
10. ANS:
dependent
PTS: 1
DIF: L2
REF: 3-1 Graphing Systems of Equations
OBJ: 3-1.1 Systems of Linear Equations STA: CA A2 2.0
TOP: 3-1 Example 3
KEY: system of linear equations | dependent system
11. ANS:
y
4
2
–4
–2
O
2
4
x
–2
–4
PTS: 1
DIF: L2
REF: 3-3 Systems of Inequalities
OBJ: 3-3.1 Solving Systems of Inequalities
STA: CA A2 1.0 | CA A2 2.0
TOP: 3-3 Example 4
KEY: system of inequalities | graphing | absolute value
12. ANS:
y
6
4
2
–6
–4
–2 O
–2
–4
–6
2
4
6
x
PTS: 1
DIF: L2
REF: 3-3 Systems of Inequalities
OBJ: 3-3.1 Solving Systems of Inequalities
STA: CA A2 1.0 | CA A2 2.0
TOP: 3-3 Example 2
KEY: system of inequalities | graphing
13. ANS:
y
8
4
–8
–4
O
4
8
x
–4
–8
PTS: 1
DIF: L3
REF: 3-3 Systems of Inequalities
OBJ: 3-3.1 Solving Systems of Inequalities
STA: CA A2 1.0 | CA A2 2.0
TOP: 3-3 Example 2
KEY: system of inequalities | graphing
14. ANS:
(1, –4)
PTS: 1
DIF: L2
REF: 3-2 Solving Systems Algebraically
OBJ: 3-2.1 Solving Systems by Substitution
STA: CA A2 2.0
TOP: 3-2 Example 1
KEY: system of linear equations | substitution method
15. ANS:
(0, –5)
PTS: 1
DIF: L2
REF: 3-2 Solving Systems Algebraically
OBJ: 3-2.1 Solving Systems by Substitution
STA: CA A2 2.0
TOP: 3-2 Example 1
KEY: system of linear equations | substitution method
16. ANS:
(2, 1, 1)
PTS: 1
DIF: L2
REF: 3-6 Systems With Three Variables
OBJ: 3-6.2 Solving Three-Variable Systems by Substitution
STA: CA A2 2.0
TOP: 3-6 Example 3
KEY: system with three variables | substitution method
17. ANS:
(–1, –6, 1)
PTS: 1
DIF: L2
REF: 3-6 Systems With Three Variables
OBJ: 3-6.2 Solving Three-Variable Systems by Substitution
STA: CA A2 2.0
TOP: 3-6 Example 3
KEY: system with three variables | substitution method
18. ANS:
(0, 0), (0, 2), (2, 0), (4, 6); maximum value of 8
PTS:
OBJ:
TOP:
KEY:
1
DIF: L3
REF: 3-4 Linear Programming
3-4.1 Finding Maximum and Minimum Values
STA: CA A2 2.0
3-4 Example 1
linear programming | constraints | vertices | objective function | maximum value
ESSAY
19. ANS:
[4] a. Let x be pounds of tuna and y be pounds of salmon.
The objective function is
and the constraints are
b.
c.
[3]
[2]
[1]
The market should buy 89.33 pounds of tuna and 0 pounds of salmon to maximize profit.
two parts correct
one part correct
correct answers, but no work shown
PTS: 1
DIF: L4
REF: 3-4 Linear Programming
OBJ: 3-4.2 Writing Linear Programs
STA: CA A2 2.0
TOP: 3-4 Example 2
KEY: maximize | objective function | vertices | word problem | problem solving | rubric-based question | extended
response | maximum value | linear programming
20. ANS:
[4] a. Let x be pounds of tuna and y be pounds of salmon.
The objective function is
and the constraints are
b.
c.
[3]
[2]
[1]
The market should buy 89.33 pounds of tuna and 0 pounds of salmon to maximize profit.
two parts correct
one part correct
correct answers, but no work shown
PTS: 1
DIF: L4
REF: 3-4 Linear Programming
OBJ: 3-4.2 Writing Linear Programs
STA: CA A2 2.0
TOP: 3-4 Example 2
KEY: maximize | objective function | vertices | word problem | problem solving | rubric-based question | extended
response | maximum value | linear programming