Answer to Question #265672 in Calculus for Cakay

Question

B & N Ltd monthly demand for shirts is given by p=1500-0.4q,where p denotes the price (in dollars) of each shirt and q denotes the quantity demanded.The company's manufacturing department estimated the total profit (in dollars) of producing q units of shirts to be P (q)=-0.4q²+1300q+1000,Calculate the price at which Buck&MaraghLtd.profit maximized.

Answer 1

profit maximized if

$P' (q)=-0.8q+1300=0$

$q=1300/0.8=1625$

$p(1625)=1500-0.4\cdot 1625=\$850$