AnswersFinancial MathLinear-Quadratic Systems

Linear-Quadratic Systems — Quiz Answers

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A software company has fixed monthly expenses of $⁢10,000 and a variable cost of $⁢100 per software license sold. Due to market capacity, revenue is $⁢0 when 0 licenses are sold and $⁢0 when 200 licenses are sold. The maximum revenue occurs when 100 licenses are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the number of software licenses sold?

A
cap c times x is equal to 10 comma 000 x plus 100 cap r times x is equal to negative x times open paren x minus 200 close paren
B
cap c times x is equal to 100 x plus 10 comma 000 cap r times x is equal to negative x times open paren x minus 100 close paren
C
cap c times x is equal to 100 x plus 10 comma 000 cap r times x is equal to negative x times open paren x minus 200 close paren
D
cap c times x is equal to 10 comma 000 x plus 100 cap r times x is equal to negative x times open paren x minus 100 close paren
62
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How many necklaces need to be sold to reach the maximum revenue?

A
30
B
25
C
20
D
45
63

Which graph represents the system of equations? y=x^2−2⁢x+1 y=x+5

A
Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (0, 5), (5, 10). Points on the curved line are (negative 1, 0), (3, 15), (5, 40).
B
Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (negative 1, 5), (4, 9), (5, 10). Points on the curved line are (negative 1, 5), (1, 0), (4, 9).
C
Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (negative 1, 0), (3, 30). Points on the curved line are (negative 1, 5), (0, 0), (4, 30).
D
Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (negative 1, 0), (0, 5), (3, 20). Points on the curved line are (negative 1, 0), (2, 9), (4, 25).
64

How many units need to be sold to maximize the store's revenue?

A
12 comma 000 units
B
16 comma 000 units
C
6 comma 000 units
D
4 comma 000 units
65

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+15⁢x−28 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=4⁢x How many units must the company sell to break even?

A
4 comma 000 or 16 comma 000 units
B
7 comma 000 or 28 comma 000 units
C
4 comma 000 or 7 comma 000 units
D
16 comma 000 or 28 comma 000 units
66

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+12⁢x−18 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=3⁢x How many units must the company sell to break even?

A
3 comma 000 or 6 comma 000 units
B
9 comma 000 or 18 comma 000 units
C
3 comma 000 or 9 comma 000 units
D
0 or 6 comma 000 units
67

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+9⁢x−10 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=2⁢x How many units must the company sell to break even?

A
2 comma 000 or 4 comma 000 units
B
5 comma 000 or 10 comma 000 units
C
2 comma 000 or 5 comma 000 units
D
4 comma 000 or 10 comma 000 units
68

What are the break-even points?

A
(9, 459) and (30, 900)
B
(9, 459) and (45, 675)
C
(0, 0) and (45, 675)
D
(0, 0) and (30, 900)
69

Which graph represents the system of equations? y=x^2−2⁢x+1 y=x+5

A
Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (negative 1, 5), (4, 9), (5, 10). Points on the curved line are (negative 1, 5), (1, 0), (4, 9).
B
Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (negative 1, 0), (0, 5), (3, 20). Points on the curved line are (negative 1, 0), (2, 9), (4, 25).
C
Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (0, 5), (5, 10). Points on the curved line are (negative 1, 0), (3, 15), (5, 40).
D
Image with description A coordinate plane with a line and a curved line. The x-axis is labeled from negative 3 to 5 and the y-axis is labeled from 0 to 50. Points on the line are (negative 1, 0), (3, 30). Points on the curved line are (negative 1, 5), (0, 0), (4, 30).
70

A farmer sells organic apples at a local market. The fixed costs are $⁢800 per season, and the variable cost is $⁢1 per kilogram of apples sold. The revenue is $⁢0 when 0 kg or 160 kg of apples are sold due to market limitations. The maximum revenue occurs when 80 kg of apples are sold. Which system of equations represents the linear cost function C⁡(x) and the quadratic revenue function R⁡(x) , where x represents the kilograms of apples sold?

A
cap c times x is equal to 800 x plus 1 cap r times x is equal to negative x times open paren x minus 80 close paren
B
cap c times x is equal to 800 x plus 1 cap r times x is equal to negative x times open paren x minus 160 close paren
C
cap c times x is equal to x plus 800 cap r times x is equal to negative x times open paren x minus 160 close paren
D
cap c times x is equal to x plus 800 cap r times x is equal to negative x times open paren x minus 80 close paren
71

What are the break-even points?

A
(0, 0) and (45, 675)
B
(9, 459) and (30, 900)
C
(0, 0) and (30, 900)
D
(9, 459) and (45, 675)
72

Part of the system of equations has been graphed. Graph the linear equation. y=x^2−2⁢x y=−x+6

Answer:

parabola; 1; -1; 0; line; 6

73

How many units need to be sold to maximize the company's revenue?

A
6 comma 000 units
B
4 comma 000 units
C
2 comma 000 units
D
3 comma 000 units
74

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+12⁢x−18 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=3⁢x How many units must the company sell to break even?

A
9 comma 000 or 18 comma 000 units
B
3 comma 000 or 6 comma 000 units
C
3 comma 000 or 9 comma 000 units
D
0 or 6 comma 000 units
75

A company's revenue, R⁡(x) , in thousands of dollars, from selling x thousand units is modeled by the quadratic function shown. R⁡(x)=−x^2+15⁢x−28 Its cost, C⁡(x) , in thousands of dollars, is modeled by the linear function C⁡(x)=4⁢x How many units must the company sell to break even?

A
16 comma 000 or 28 comma 000 units
B
4 comma 000 or 7 comma 000 units
C
7 comma 000 or 28 comma 000 units
D
4 comma 000 or 16 comma 000 units
76

Part of the system of equations has been graphed. Graph the linear equation. y=x^2−6⁢x+8 y=x−4

Answer:

parabola; 3; -1; 0; 8; line; -4; 4

77

How many necklaces need to be sold to reach the maximum revenue?

A
25
B
30
C
20
D
45
78

Part of the system of equations has been graphed. Graph the linear equation. y=x^2−6⁢x+8 y=x−4

Answer:

parabola; 3; -1; 0; 8; line; -4; 4

79

When does the maximum revenue occur?

Answer:

25

80

How many units must the restaurant sell to break even?

A
0 or 4 comma 000 units
B
2 comma 000 or 4 comma 000 units
C
1 comma 000 or 5 comma 000 units
D
0 or 5 comma 000 units

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