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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
+2541
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$$x =$$  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
+124696
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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

Apr 16, 2022