An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.
Use these values to determine the maximum value of the objective function and the values of x and y for which the
maximum occurs.
176)
Objective Function z = 6x + 7y
Constraints x 0
y 0
2x + 3y 12
2x + y
8
176)
A)
Maximum 24; at (4, 0)
B)
Maximum 52; at (4, 4)
C)
Maximum 32; at (3, 2)
D)
Maximum 32; at (2, 3)
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
177)
9x – 8y =2
–36x + 32y = – 6
177)
A)
{(4, 3)}
B)
27
4, –6
C)
{(x, y) 9x – 8y =2 }
D)
D
Solve the system by the substitution method.
178)
xy = 1
48x – y = – 2
178)
A)
1
8, 8
B)
–1
6, –6, 1
8, 8
C)
{(6, –6), (–8, 8)}
D)
–6, –1
6, 8, 1
8
B
79
C
Determine whether the given ordered pair is a solution of the system.
179)
(5, 6)
4x + y =26
2x + 4y =34
179)
A)
not a solution
B)
solution
Write the partial fraction decomposition of the rational expression.
180)
5x2+ 7x + 4
x3+ 3x2+ 5x + 15
180)
A)
2
x + 3 +3
x2+ 5
B)
2
x + 3 +3
x + 5 +
–2
(x + 5)2
C)
2
x + 3 +3x – 2
x2+ 5
D)
2
x + 5 +3x – 2
x2+ 3
C
Solve the problem.
181)
Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 6 hours to
make a hat and 4 hours to make an afghan, and she has no more than 52 hours available. She has
material for no more than 11 items and no more than 8 afghans. The bazaar will sell the hats for $13
each and the afghans for $7 each. How many of each should she make to maximize the income for
the bazaar? What is the maximum income?
181)
A)
6 hats and 5 afghans; $113
B)
8 hats and 3 afghans; $125
C)
7 hats and 4 afghans; $119
D)
4 hats and 7 afghans; $101
D
Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many
solutions, using set notation to express their solution sets.
182)
x – 6y =13
2x – 7y =21
182)
A)
{(6, 0)}
B)
{(7, –1)}
C)
{(x, y) x – 6y =13}
D)
B
80
B
Solve the problem.
183)
In 1985, in the town of Appleby, 19.4% of Hispanics were overweight, increasing by an average of
0.41% per year. In 1985, in the town of Appleby, 0.15% of whites were overweight, increasing by
an average of 32.0% per year. If these trends continue, in which year will the percentage of
Hispanics who are overweight be the same as the percentage of whites who are overweight?
Round to the nearest year. What percentage of Hispanics (to the nearest whole percent) will be
overweight at that time?
183)
A)
1982; 18%
B)
1986; 20%
C)
1984; 19%
D)
1988; 20%
Solve the system by the addition method.
184)
2x + 20y = – 144
11x + 5y =48
184)
A)
{(–8, 8)}
B)
{(8, –8)}
C)
{(–5, 8)}
D)
{(11, –11)}
D)
185)
x2–y2=3
x2+y2=9
185)
A)
{( 6, 3), (–6, 3)}
B)
{( 6, 3), (–6, –3)}
C)
{( 6, 3), (–6, 3), ( 6, –3), (–6, –3)}
D)
{(0, 0)}
D)
Graph the solution set of the system of inequalities or indicate that the system has no solution.
186)
x + 3y 6
x > – 2
y 6
186)
81
D)
A)
B)
C)
D)
Solve the system by the addition method.
187)
x2+y2=9
9x2+16y2=144
187)
A)
{(3, 0), (–3, 0)}
B)
{(0, 3), (0, –3)}
C)
{(4, 0), (–4, 0)}
D)
{(0, 4), (0, –4)}
82
Solve the problem.
188)
Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 7 hours to
make a hat and 2 hours to make an afghan, and she has no more than 35 hours available. She has
material for no more than 10 items, and she wants to make at least two afghans. Let x = the number
of hats she makes and y = the number of afghans she makes. Write a system of inequalities that
describes these constraints.
188)
A)
7x +2y 35
x + y 10
y 2
B)
7x +2y 35
x + y 10
y 2
C)
7x +2y 35
x + y 10
x 2
D)
2x +7y 35
x + y 10
x 2
Solve the system of equations by the substitution method.
189)
–9x + y =5
–3x – 4y = – 7
189)
A)
–4, –3
2
B)
{(1, –1)}
C)
–1
3, 2
D)
2
3, 11
Solve the problem.
190)
One number is 7 less than a second number. Twice the second number is 2 less than 4 times the
first. Find the two numbers.
190)
A)
8 and 15
B)
9 and 16
C)
7 and 14
D)
–15 and –8
Solve the system of equations by the substitution method.
191)
x + y =6
y=2x
191)
A)
{(–2, –4)}
B)
{(2, 4)}
C)
{(2, –4)}
D)
{(–2, 4)}
83
Determine whether the given ordered pair is a solution of the system.
192)
(–6, 2)
4x = – 22 – y
2x = – 4– 4y
192)
A)
solution
B)
not a solution
An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed region.
Use these values to determine the maximum value of the objective function and the values of x and y for which the
maximum occurs.
193)
Objective Function z = 7x + 6y
Constraints x 0
y 0
3x + y
21
x + y
10
x + 2y
12
193)
A)
Maximum 68; at (8, 2)
B)
Maximum 66; at (6, 4)
C)
Maximum 60; at (6, 3)
D)
Maximum 65.5; at (5.5, 4.5)
D)
Let x represent one number and let y represent the other number. Use the given conditions to write a system of nonlinear
equations. Solve the system and find the numbers.
194)
The sum of the squares of two numbers is 40. The difference of the two numbers is 8. Find the two
numbers.
194)
A)
–6 and 2
B)
–2 and 6; –6 and 2
C)
–6 and –2; 2 and 6
D)
–2 and 6
D)
Graph the inequality.
195)
y + 4 < x
195)
84
A)
B)
C)
D)
Write the partial fraction decomposition of the rational expression.
196)
8x2–8x +5
(x– 1)3
196)
A)
8
x – 1 –8
(x– 1)2+5
(x– 1)3
B)
8
x – 1 +8
(x– 1)2+5
(x– 1)3
C)
8
x – 1 +8
(x– 1)2
D)
8
x – 1 +x +8
(x– 1)2+x2+5
(x– 1)3
85
Determine if the given ordered triple is a solution of the system.
197)
(2, 5, –3)
x + y + z =4
x – y + 3z = – 2
2x + y + z =1
197)
A)
solution
B)
not a solution
Write the partial fraction decomposition of the rational expression.
198)
–3x2– 13x – 12
(x + 2)(x + 1)2
198)
A)
–2
x + 2 +
–5
x + 1 +2
(x + 1)2
B)
–2
x + 2 +
–5
x + 1 +
–2
(x + 1)2
C)
2
x + 2 +
–5
x + 1 +
–2
(x + 1)2
D)
2
x + 2 +5
x + 1 +
–2
(x + 1)2
Graph the inequality.
199)
x2+y249
199)
A)
B)
86
C)
D)
Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of feasible points.
200)
Objective Function: z =9x + 10y
Find minimum.
200)
A)
minimum: 68
B)
minimum: 56
C)
minimum: 57
D)
no minimum
Solve the system by the addition method.
201)
y2+4x2=21
y2–x2= 1
201)
A)
(2, 5), (2, –5)
B)
(3, 5), (3, –5), (–3, 5), (–3, –5)
C)
(3, 5), (3, –5)
D)
(2, 5), (2, –5), (–2, 5), (–2, –5)
87
Find the maximum or minimum value of the given objective function of a linear programming problem. The figure
illustrates the graph of feasible points.
202)
Objective Function: z = – 8x – y
Find maximum.
202)
A)
maximum: –34
B)
maximum: –27
C)
maximum: –21
D)
no maximum
Solve the problem.
203)
In a 1–mile race, the winner crosses the finish line 11 feet ahead of the second–place runner and 29
feet ahead of the third–place runner. Assuming that each runner maintains a constant speed
throughout the race, by how many feet does the second–place runner beat the third–place runner?
(5280 feet in 1 mile.)
203)
A)
–18.1 ft
B)
7.01 ft
C)
18.04 ft
D)
–11.06 ft
204)
Johnny’s cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides
790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories.
Find the caloric content of each item.
204)
A)
Serving of ice cream: 250 calories
Serving of blueberry pie: 270 calories
B)
Serving of ice cream: 230 calories
Serving of blueberry pie: 280 calories
C)
Serving of ice cream: 256 calories
Serving of blueberry pie: 267 calories
D)
Serving of ice cream: 270 calories
Serving of blueberry pie: 250 calories
88
The figure shows the graphs of the cost and revenue functions for a company that manufactures and sells binoculars. Use
the information in the figure to answer the question.
205)
Use the revenue and cost functions to write the profit function from producing and selling x
binoculars.
205)
A)
P(x) = 4x – 1500
B)
P(x) = 2x + 1500
C)
P(x) = 4x + 1500
D)
P(x) = 2x – 1500
Solve the problem.
206)
A dietitian needs to purchase food for patients. She can purchase an ounce of chicken for $0.25 and
an ounce of potatoes for $0.02. The dietician is bound by the following constraints.
· Each ounce of chicken contains 13 grams of protein and 24 grams of carbohydrates.
· Each ounce of potatoes contains 5 grams of protein and 35 grams of carbohydrates.
· The minimum daily requirements for the patients under the dietitian‘s care are 45 grams of
protein and 58 grams of carbohydrates.
Let x = the number of ounces of chicken and y = the number of ounces of potatoes purchased per
patient. Write a system of inequalities that describes these constraints.
206)
A)
13x +24y 45
5x +35y 58
B)
13x +5y 58
24x +35y 45
C)
13x +24x 45
5y +35y 58
D)
13x +5y 45
24x +35y 58
89
Solve the system by the substitution method.
207)
x – 2y = 3
x2– xy = 20
207)
A)
{(–5, –1), (8, 11
2)}
B)
{(5, 1), (–11
2, –8)}
C)
{(–5, –1), ( 11
2, 8)}
D)
{(5, 1), (–8, –11
2)}
Decide if the system of equations in two variables is linear or nonlinear.
208)
xy = – 8
x +9y =3
208)
A)
Linear
B)
Nonlinear
Explanation:
Solve the system by the addition method.
209)
3x2+y2=9
3x2–y2=9
209)
A)
{( 3, 0), (–3, 0)}
B)
{(0, 3), (0, –3)}
C)
{(0, 3), (0, –3)}
D)
{(3, 0), (–3, 0)}
Explanation:
90
Explanation:
Answer Key
Testname: C5
Answer Key
Testname: C5
Answer Key
Testname: C5
Answer Key
Testname: C5
Answer Key
Testname: C5
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