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Linear-Quadratic Systems — Quiz Answers

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What are the break-even points?

A
(2, 76) and (20, 400)
B
(0, 0) and (20, 400)
C
(2, 76) and (34, 204)
D
(0, 0) and (34, 204)
44

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

A
6 comma 000 units
B
16 comma 000 units
C
4 comma 000 units
D
12 comma 000 units
47

What are the break-even points?

A
(2, 76) and (34, 204)
B
(0, 0) and (20, 400)
C
(2, 76) and (20, 400)
D
(0, 0) and (34, 204)
48

What are the break-even points?

A
(0, 0) and (34, 204)
B
(2, 76) and (20, 400)
C
(2, 76) and (34, 204)
D
(0, 0) and (20, 400)
49

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 100 x plus 10 comma 000 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 10 comma 000 x plus 100 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 10 comma 000 x plus 100 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 100 x plus 10 comma 000 cap r times x is equal to negative x times open paren x minus 100 close paren
51

A boutique owner sells handcrafted scarves. The fixed monthly costs are $⁢500 , and the variable cost per scarf is $⁢10 The boutique's revenue is $⁢0 when 0 scarves are sold and $⁢0 when 100 scarves are sold due to market saturation. The maximum revenue occurs when 50 scarves 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 scarves sold?

A
cap c times x is equal to 500 x plus 10 cap r times x is equal to negative x times open paren x minus 50 close paren
B
cap c times x is equal to 500 x plus 10 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 10 x plus 500 cap r times x is equal to negative x times open paren x minus 100 close paren
D
cap c times x is equal to 10 x plus 500 cap r times x is equal to negative x times open paren x minus 50 close paren
53

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
59

How many units must the restaurant sell to break even?

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

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