A traveling circus is evaluating its pricing policy for the next town it will visit. Demand comes from two sources: children (under 12) and adults.

The demand from children and its inverse are given by

Qc =60060.Pc PCc=10 1/60.Qc

The demand from adults and its inverse are given by

Qa=80025Pa Pa=32 1/25Qa

The circus management people are experienced at identifying whether a person is under 12 or not, and so are able to charge a different price for children under 12 than for other people.

The marginal cost per adult is zero, but the marginal cost per child under 12 is $1 because each child under 12 gets a free gift.

The circus tent cannot accommodate more than 750 total people (children plus adults).

Q. What are the profit-maximizing quantities and prices?