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?
Answer
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 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 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 100 x plus 10 comma 000 cap r times x is equal to negative x times open paren x minus 100 close paren
Explanation
The cost function adds the fixed monthly expense of $10,000 to $100 for each license, so C(x) = 100x + 10,000. Revenue is zero at x = 0 and x = 200, so its factors are x and (x − 200). The maximum is halfway between those zeros, at x = 100, and the revenue parabola must open downward; thus R(x) = −x(x − 200). Choice C gives both functions.
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