+81 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 8,000 fewer tickets a week. How many dollars should they charge to maximize their total revenue?
+1262 squares are the largest so we want to maximize it by making a chart
200*40000=8000000
210*32000=6720000
220*24000=5280000
we see that 8000000 is greatest so our final answer is 8000000
+36916 EDITED
currently $ 200 x 40 000
200 + 10x is the number of 10 dollar price increses (x)
tickets will be 40 000 - 8000x
revenue will be price x # tix = (200+ 10x)(40 000- 8000x) and we want the max of this
expanding 8 000 000 - 1,600,000x + 400,000x - 80,000x^2
re-arranging - 80,000 x^2 -1,200,000x + 8 000 000 = REVENUE
MAX WILL OCCUR AT x = -b/2a = - - 1 200 000 /(2*(-80,000) ) = -7.5
tells us increasing the price AT ALL willl result in a decrease in revenue !
If they DECREASE the ticket price 7.5 x 10 = $ 75
to $125 they will max revenue at $ 12,500,000
