Question

A company manufacturers and sells x electric drills per month. The monthly cost and price-demand equations are C(x)=73000+40x,
p=220−x/30, 0<=x<=5000.

(A) Find the production level that results in the maximum profit.
Production Level =

(B) Find the price that the company should charge for each drill in order to maximize profit.
Price =

Answer 1

profit = demand - cost
\[
P(x)=\left(200-{x\over30}\right)-(73000+40x)
\]simplify this equation.
at maximum profit, its first derivative is "0"
so, we take the derivative and set it to "0" and solve for "x"