When the admission price for a baseball game was $30 per ticket, 36,000 tickets were sold. When the price was raised to $35, only 32,000 tickets were sold. Assume that the demand function is linear and that the marginal and fixed costs for the ballpark owners are $5 and $700,000, respectively.

(a) Find the profit P as a function of x, the number of tickets sold.

P=

(b) Find the marginal profits, in dollars per ticket, when 18,000 tickets are sold, when 28,000 tickets are sold, and when 32,000 tickets are sold.

P'(18,000)=$ per ticket

P'(28,000)=$ per ticket

P'(32,000)=$ per ticket