A manufacturing company sells high quality jackets through a chain of specialty shops. the demand equation for this jackets is

Question

p = 400 − 50q
where p is the selling price ( in dollars per jacket) and q is the demand ( in thousands of jackets). If this company’s marginal cost function is given by
dc/dq =800/q + 5
show that there is a maximum profit, and determine the number of jackets that must be sold to obtain the maximum profit.

Answer 1

revenue = q*p(q) = 400q - 50q^2
So the profit is
P(q) = (400q - 50q^2) - c(q)
dP/dq = 400 - 100q - (800/q + 5)
Hmmm. dP/dq is never zero. Better check my math.