sunnys ice cream parlor sells cones, with revenue given by $r(q)=5q$ and cost given by $c(q)=120+\frac{1}{20}…

sunnys ice cream parlor sells cones, with revenue given by $r(q)=5q$ and cost given by $c(q)=120+\frac{1}{20}q^{2}$, where $q$ is the number of cones sold per day. profit is defined as $p(q)=r(q)-c(q)$. what is the expression for the rate of change of profit with respect to quantity, $p(q)$? $p(q)=$

sunnys ice cream parlor sells cones, with revenue given by $r(q)=5q$ and cost given by $c(q)=120+\frac{1}{20}q^{2}$, where $q$ is the number of cones sold per day. profit is defined as $p(q)=r(q)-c(q)$. what is the expression for the rate of change of profit with respect to quantity, $p(q)$? $p(q)=$

Answer

Explanation:

Step1: Find the profit function

$P(q)=R(q)-C(q)=5q-(120 + \frac{1}{20}q^{2})=5q - 120-\frac{1}{20}q^{2}$

Step2: Differentiate the profit function

Using the power - rule $\frac{d}{dq}(ax^{n})=nax^{n - 1}$, for $P(q)=5q - 120-\frac{1}{20}q^{2}$, we have: $\frac{dP}{dq}=P'(q)=\frac{d}{dq}(5q)-\frac{d}{dq}(120)-\frac{d}{dq}(\frac{1}{20}q^{2})$ $P'(q)=5-0-\frac{1}{20}\times2q$ $P'(q)=5-\frac{1}{10}q$

Answer:

$5-\frac{1}{10}q$