find the profit function if cost and revenue are given by c(x)=132 + 5.8x and r(x)=6x - 0.07x^2. the profit…
find the profit function if cost and revenue are given by c(x)=132 + 5.8x and r(x)=6x - 0.07x^2. the profit function is p(x)=□.
Answer
Explanation:
Step1: Recall profit - revenue - cost formula
The profit function $P(x)$ is given by $P(x)=R(x)-C(x)$.
Step2: Substitute the given functions
Substitute $C(x)=132 + 5.8x$ and $R(x)=6x-0.07x^{2}$ into the profit - formula: $P(x)=(6x - 0.07x^{2})-(132 + 5.8x)$.
Step3: Simplify the expression
$P(x)=6x-0.07x^{2}-132 - 5.8x$. Combine like - terms: $P(x)=-0.07x^{2}+(6x - 5.8x)-132$. $P(x)=-0.07x^{2}+0.2x - 132$.
Answer:
$-0.07x^{2}+0.2x - 132$