find the profit function if cost and revenue are given by c(x)=196 + 2.4x and r(x)=6x - 0.03x^2. the profit…
find the profit function if cost and revenue are given by c(x)=196 + 2.4x and r(x)=6x - 0.03x^2. the profit function is p(x)=□.
Answer
Explanation:
Step1: Recall profit - revenue formula
The profit function $P(x)$ is given by $P(x)=R(x)-C(x)$.
Step2: Substitute the given functions
Substitute $R(x) = 6x-0.03x^{2}$ and $C(x)=196 + 2.4x$ into the profit - formula: $P(x)=(6x-0.03x^{2})-(196 + 2.4x)$.
Step3: Simplify the expression
$P(x)=6x-0.03x^{2}-196 - 2.4x$. Combine like - terms: $P(x)=-0.03x^{2}+(6x - 2.4x)-196$. $P(x)=-0.03x^{2}+3.6x - 196$.
Answer:
$-0.03x^{2}+3.6x - 196$