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. show full work.