question 24 of 40 the revenue, in thousands of dollars, that a company earns selling lawnmowers can be…

question 24 of 40 the revenue, in thousands of dollars, that a company earns selling lawnmowers can be modeled by r(x)=90x - x² and the companys total profit, in thousands of dollars, after selling x lawnmowers can be modeled by p(x)= -x² + 30x - 200. which function represents the companys cost, in thousands of dollars, for producing lawnmowers? (recall that profit equals revenue minus cost.) a. c(x)=2x² + 60x + 200 b. c(x)= -2x² - 60x - 200 c. c(x)=60x + 200 d. c(x)= -60x² - 200

question 24 of 40 the revenue, in thousands of dollars, that a company earns selling lawnmowers can be modeled by r(x)=90x - x² and the companys total profit, in thousands of dollars, after selling x lawnmowers can be modeled by p(x)= -x² + 30x - 200. which function represents the companys cost, in thousands of dollars, for producing lawnmowers? (recall that profit equals revenue minus cost.) a. c(x)=2x² + 60x + 200 b. c(x)= -2x² - 60x - 200 c. c(x)=60x + 200 d. c(x)= -60x² - 200

Answer

Explanation:

Step1: Recall profit formula

We know that $P(x)=R(x)-C(x)$, where $P(x)$ is profit, $R(x)$ is revenue and $C(x)$ is cost. So, $C(x)=R(x)-P(x)$.

Step2: Substitute given functions

Given $R(x)=90x - x^{2}$ and $P(x)=-x^{2}+30x - 200$. Then $C(x)=(90x - x^{2})-(-x^{2}+30x - 200)$.

Step3: Simplify the expression

[ \begin{align*} C(x)&=90x - x^{2}+x^{2}-30x + 200\ &=( - x^{2}+x^{2})+(90x-30x)+200\ &=60x + 200 \end{align*} ]

Answer:

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