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?

toodlestraws Jul 29, 2020

#1**+1 **

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

jimkey17 Jul 29, 2020

#3**+1 **

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

ElectricPavlov Jul 29, 2020

edited by
ElectricPavlov
Jul 29, 2020

edited by ElectricPavlov Jul 29, 2020

edited by ElectricPavlov Jul 29, 2020

edited by ElectricPavlov Jul 29, 2020

edited by ElectricPavlov Jul 29, 2020