A specialty coffee roaster faces the demand function p(q)=50−0.2q for selling q pounds of coffee per week. The weekly cost of producing q pounds is modeled by
C(q)=10q+300,
where C(q) is measured in dollars.
Respond to all parts below.
(a) Write an explicit formula for the weekly profit P(q).
(b) Determine the weekly production level q that maximizes profit. Show all calculus justification.
(c) Find the corresponding selling price per pound.
(d) Compute the maximum weekly profit and interpret its meaning in context.