A study of a country's colleges and universities resulted in the demand equation q = 20,000 2p, where q is the enrollment at a public college or university and p is the average annual tuition (plus fees) it charges. Officials at Enormous State University have developed a policy whereby the number of students it will accept per year at a tuition level of p dollars is given by q = 8,700 + 0.5p. Find the equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level. What is the total social gain at the equilibrium price? HINT [See Example 3.]

equilibrium tuition price	p		=	$
consumers' surplus	CS		=	$
producers' surplus	PS		=	$
total social gain				$