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?

Guest Apr 16, 2022

#1**+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: \(200 +32 \times 1 2 = \color{brown}\boxed{584}\)

BuilderBoi Apr 16, 2022

#2**+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

CPhill Apr 16, 2022