Question

question 31 of 40
the revenue, in thousands of dollars, that a company earns selling
lawnmowers can be modeled by \\( \mathrm{r}(x) = 90x - x^2 \\) and the companys total
profit, in thousands of dollars, after selling \\( x \\) lawnmowers can be modeled by
\\( \mathrm{p}(x) = -x^2 + 30x - 200 \\). which function represents the companys cost,
in thousands of dollars, for producing lawnmowers? (recall that profit equals
revenue minus cost.)

\\( \bigcirc \\) a. \\( \mathrm{c}(x) = -2x^2 - 60x - 200 \\)

\\( \bigcirc \\) b. \\( \mathrm{c}(x) = 2x^2 + 60x + 200 \\)

\\( \bigcirc \\) c. \\( c(x) = 60x + 200 \\)

\\( \bigcirc \\) d. \\( \mathrm{c}(x) = -60x^2 - 200 \\)

Explanation:

Step1: Recall profit formula

Profit = Revenue - Cost → \( C(x) = R(x) - P(x) \)

Step2: Substitute given functions

\( C(x) = (90x - x^2) - (-x^2 + 30x - 200) \)

Step3: Simplify the expression

\( C(x) = 90x - x^2 + x^2 - 30x + 200 = 60x + 200 \)

Answer:

C. \( C(x) = 60x + 200 \)