An airplane with a 100-passenger capacity is to be chartered for a flight to Nevada. The airplane cannot be chartered unless there are at least 50 passengers. The cost of the trip is $340 per passenger, except that the airline company agrees to reduce everyone’s ticket price by $2 for each ticket sold in excess of 50. Let x be the number of tickets sold in excess of 50 (i.e. 56 tickets sold means x = 6) and let f(x) be the total ticket income that the company will receive. (20 points total)
a) Write a function that expresses the total ticket income.
b) How much income will the company generate if they sell 60 tickets?
c) How many tickets does the company want to sell to maximize the income?

Question

An airplane with a 100-passenger capacity is to be chartered for a flight to Nevada. The airplane cannot be chartered unless there are at least 50 passengers. The cost of the trip is $340 per passenger, except that the airline company agrees to reduce everyone’s ticket price by $2 for each ticket sold in excess of 50. Let x be the number of tickets sold in excess of 50 (i.e. 56 tickets sold means x = 6) and let f(x) be the total ticket income that the company will receive. (20 points total) 			 
a)	Write a function that expresses the total ticket income. 
b)	How much income will the company generate if they sell 60 tickets?
c)	How many tickets does the company want to sell to maximize the income?