Question

Do It Yourself Diet Systems sells a weight monitoring and control system so that you don't have to prepare all those healthy foods that you are actually supposed to be eating if you're on a diet. It estimates the monthly quantity demanded for its complete kit to be represented by the equation:

P = 944 - 11Q, where P is the price of the whole kit.

Its monthly cost function is

STC = 10,000 + 44Q + 4Q2.

Determine the profit maximizing quantity sold and the price for the kit.

How much will the maximum monthly profit be?

Answer 1

The profit maximizing quantity is at the quantity where Marginal revenue equal marginal cost .

P = 944 - 11Q

TR = 944Q - 11Q^2

MR = 944 - 22Q

STC = 10,000 + 44Q + 4Q^2

MC = 44 + 8Q

944 - 22Q = 44 + 8Q

900 = 30Q

Q = 30

P = 944 - 11*30 = $614

maximum monthly profit = TR -TC

profit = (30 * 614 ) - 10,000 + 44*30  + 4*30^2

profit = 18420 ) - 14920

profit = $ 3500