GetThere Airlines currently charges 200 dollars per ticket and sells 40,000 tickets a week. For every 10 dollars they increase the ticket price, they sell 100 fewer tickets a week. How many dollars should they charge to maximize their total revenue?
+36916 # of ten dollar increase in tix price = x
revenue = (40 000 - 100x)(200 + 10x)
( 8 000 000 + 400 000x - 20 000x - 10 000x^2 )
(-10 000 x^2 + 380 000 x + 8 000 000) this is a dome shaped parabola (due to the negative coefficient for x^2)
max will occur at x = -b/2a = 380 000/ (10 000(2)) = 19
19 ten dollar increases will make ticket price = 200 + 190 = 390 dollars
