Question

The Children’s Theatre Company (CTC) in Minneapolis produces high quality theater for kids. Demand for tickets can be expressed by the following equation P= 40-(Q/50) where Q is the number of tickets sold and P is the price per ticket. The only cost of staging a production is $10,000 per night and is independent of the size of the audience (a fixed cost). Therefore, the marginal cost is $0.

What is their max profit?

Answer 1

Answer

Profit = TR - TC

where TR = Total revenue = P*Q = (40-(Q/50))Q and TC = Total Cost = Fixed cost + Variable cost = 10,000 + 0 = 10,000.

=> Profit = (40-(Q/50))Q - 10,000 :

Maximize : Profit

First order condition d(Profit)/dQ = 0 => 40 - 2*Q/50 - 0 = 0

=> Q = 40*25 = 1000

Hence

Profit = (40-(1000/50))1000 - 10,000 =10,000

Hence, Maximum Profit = $10000