The local space museum has hired you to assist them in setting admission prices. The museum’s managers recognize that there are two distinct demand curves for admission. One demand curve applies to people ages 12 to 64, whereas the other is for children and senior citizens. The two demand curves are: 

PA = 9.6 – 0.08QA 

PCS = 4 – 0.05QCS, 

where PA is the adult price, PCS is the child/senior citizen price, QA is the adult quantity, and QCS is the child/senior citizen quantity. Crowding is not a problem at the museum, so managers consider marginal cost to be zero. 

a. What price should they charge to each group to maximize profits?

b. How many adults will visit the museum? How many children and senior citizens? 

c. What are the museum’s profits?