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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?

 Jul 29, 2020
 #1
avatar+1130 
+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

 Jul 29, 2020
 #2
avatar+1130 
0

i mean they charge 200 dollars per week to get 8000000

jimkey17  Jul 29, 2020
 #6
avatar+26735 
0

Be careful with this method....  you may miss the peak between data points!!!

ElectricPavlov  Jul 30, 2020
 #7
avatar+1130 
0

Oh we can decrease

jimkey17  Jul 30, 2020
 #3
avatar+26735 
+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

 Jul 29, 2020
edited by ElectricPavlov  Jul 29, 2020
edited by ElectricPavlov  Jul 29, 2020
edited by ElectricPavlov  Jul 29, 2020
 #4
avatar+1130 
0

Um if it's 15 tens then the tickets they sell will be negative

jimkey17  Jul 29, 2020
 #5
avatar+26735 
0

THAT is why I was editing.......

ElectricPavlov  Jul 29, 2020

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