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avatar+979 

Usher fairs currently charges 200 dollars per entry ticket and sells 40,000 entry tickets a week. For every 10 dollars they increase the ticket price, they sell 800 fewer tickets a week. How many dollars should they charge to maximize their total revenue?

 Nov 22, 2020
 #1
avatar+116126 
+2

Let x  be the  number  of $10 increases

 

Tickets sold * Price  = Revenue

 

We have this

 

(40000 - 800x) ( 200 + 10x)   = Revenue          simplify

 

40000(200) - (800 * 200)x + ( 40000*10)x + 8000x^2      = Revenue

 

8000000 - 160000x + 400000x  - 8000x^2  = Revenue

 

R  = -8000x^2  + 240000x + 8000000  

 

To maximize  the revenue....the number of $10   increases  = x =      -240000/(-2 * -8000)  =  15

 

So....the price of a ticket that maxes the revenue =  (200 + 15*10)  = 200 + 150  =  $350

 

cool cool cool

 Nov 22, 2020
 #2
avatar+979 
+1

Thanks!

qwertyzz  Nov 22, 2020

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