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GetThere Airlines currently charges 200 dollars per ticket and sells 40,000 tickets a week. For every 12 dollars they increase the ticket price, they sell 500 fewer tickets a week. How many dollars should they charge to maximize their total revenue?

 Apr 16, 2022
 #1
avatar+2437 
+1

\(x =\)  The number of times GetThere Airlines increases the ticket cost by \($12\)

 

Write as an equation: \((200+12x)(40,000-500x)\)

 

Simplify: \(−6000x^2+380000x+8000000\)

 

The vertex appears at \(-380000\div -12000 = 31 {2 \over 3} \approx 32\)

 

Thus, they make the most money when the tickets are priced at: \(200 +32 \times 1 2 = \color{brown}\boxed{584}\)

 Apr 16, 2022
edited by BuilderBoi  Apr 16, 2022
 #2
avatar+124594 
+1

Let  x  be the number of $12 increases

 

R =  Tickets sold *  Cost per ticket

 

R =  ( 40000 - 500x) ( 200 + 12x)

 

R =  8000000 - 100000x + 480000x - 6000x^2

 

R  =   -600x^2 + 380000x + 8000000

 

The  number of  $12 increases  (which is an integer ) that max the revenue =   [  -380000 / [ 2(-6000)] ] = 31 + 2/3    ≈  32

 

The cost per ticket that maxes the revenue ≈   (200 + 12 *32)  ≈ $584

 

 

cool cool cool

 Apr 16, 2022

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