An amusement park, whose customer set is made up of two markets, adults and children, has developed demand schedules as follows:

The marginal operating cost of each unit of quantity is $5. (Hint: Because marginal cost is a constant, so is average variable cost. Ignore fixed cost.) The owners of the amusement park want to maximize profits.
a. Calculate the price, quantity, and profit if
1. The amusement park charges a different price in each market.
2. The amusement park charges the same price in the two markets combined.
3. Explain the difference in the profit realized under the two situations.
b. (Mathematical solution) The demand schedules presented in Problem 2 can be expressed in equation form as follows (where subscript A refers to the adult market, subscript G to the market for children, and subscript T to the two markets combined):

Solve these equations for the maximum profit that the amusement park will attain when it charges different prices in the two markets and when it charges a single price for the combined market.

Quantity Price (S) Children 20 18 Adults 12 10 10 12 2-20-1P 50 3P