it is assumed that the toothpaste market is perfectly competitive and the current price of a case of toothpaste is 42.00. CPI (the company) has estimated its marginal cost function to be as follows: MC (Marginal Costs) =.006Q (Quantity).
The board would like to know how many cases of toothpaste should be produced in order to maximize profits
In calculus terms,
Profit=P(q)=42q-0.006q*q
dP(q)/dq = 42-0.012q = 0
q=42/0.012=3500 cases.