Hi can anyone help me solve this question please? Airline Revenue. An airline co

Question

Hi can anyone help me solve this question please?

Airline Revenue. An airline company flies about 25,000 passengers from J.F.K. NY to Canada monthly at the price of $530 per roundtrip ticket. Current market research predicts that for each $5 increase in ticket price the number of passengers will drop by 150. Find the equation which gives the number of passengers in terms of the ticket price. Find the revenue equation. Find the price for which the revenue is maximized. Create a strong argument against having price set at $729.99. (You might want to make a table and present few values assigning one column to the price of the ticket, then number of passengers, and finally revenue)

Explanation / Answer

Number of passengers = 25000

Marginal value of number of passengers with respect to change in ticket price = -150/5 = $ (-30) per passenger

Relation between number of passengers (N) and ticket price (P)

N - 25000 = (-30) (P - 530)

N = 25000 - 30 P + 15900

N = 40900 - 30P

so Revenue R = N * P = (40900 - 30P) * P = 40900 P - 30P2

We have to find the price for which revenue is maximized

it will be when dR/ dP = 0

40900 - 60 P = 0

P= 681.67

Maximum Revanue R = 40900 * 681.67 - 30 * 681.672 = 13940083

for a price set of $ 729.99

The revenue is R = 40900 * 729.99 - 30 * 729.992 = 13870028

so we see that revenue will fall as we go beyong the optimum value of price so seting high price of 729.99 is not a good choice at all.

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