0:00
Calculus for Scientists and Engineers: Early Transcendental
Average and marginal profit Let $C(x)$ represent the cost of producing $x$ items and $p(x)$ be the sale price per item if $x$ items are sold. The profit $P(x)$ of selling $x$ items is $P(x)=x p(x)-C(x)$ (revenue minus costs). The average profit per item when $x$ items are sold is $P(x) / x$ and the marginal profit is dP/dx. The marginal profit
approximates the profit obtained by selling one more item given that $x$
items have already been sold. Consider the following cost functions $C$ and price functions $p$
a. Find the profit fiunction $P$.
b. Find the average profit function and marginal profit function.
c. Find the average profit and marginal profit if $x=$ a units have been sold.
d. Interpret the meaning of the values obtained in part (c).
$$\begin{aligned}
&C(x)=-0.04 x^{2}+100 x+800, p(x)=200-0.1 x\\
&a=1000
\end{aligned}$$
