8. the cost function for a telephone manufacturing plant is c(x)=5x + 24 and the revenue function is r(x)=…

8. the cost function for a telephone manufacturing plant is c(x)=5x + 24 and the revenue function is r(x)= - 2x²+27x, where x is the number of telephones sold, in thousands. a) determine the profit function for the number of phones sold. 2t

8. the cost function for a telephone manufacturing plant is c(x)=5x + 24 and the revenue function is r(x)= - 2x²+27x, where x is the number of telephones sold, in thousands. a) determine the profit function for the number of phones sold. 2t

Answer

Explanation:

Step1: Recall profit - function formula

Profit function $P(x)=R(x)-C(x)$, where $R(x)$ is revenue function and $C(x)$ is cost function.

Step2: Substitute given functions

Given $R(x)=-2x^{2}+27x$ and $C(x)=5x + 24$. Then $P(x)=(-2x^{2}+27x)-(5x + 24)$.

Step3: Simplify the expression

$P(x)=-2x^{2}+27x - 5x-24=-2x^{2}+(27x - 5x)-24=-2x^{2}+22x - 24$.

Answer:

$P(x)=-2x^{2}+22x - 24$ (in thousands)