Question

For a particular flight from Dulles to SF, an airline uses wide-body jets with a capacity of 370 passengers. It costs the airline $4,000 plus $145 per passenger to operate each flight. Through experience the airline has discovered that if a ticket price is $T, then they can expect (370−0.56T) passengers to book the flight. Determine the ticket price, T, that will maximize the airline's profit

Answer 1

The ticket price, T, that will maximize the airline's profit is $402.86.

Step-by-step explanation:

This can be determined as follows:

Number of passenger = (370−0.56T)

Cost = 4000 + (145 * Number of passenger) = 4000 + 145(370−0.56T) = 4000 + 53,650.00 - 81.20T = 57650 – 81.20T

Revenue = T * Number of passenger = T(370 – 0.56T) = 370T – 0.56T^2

P = Profit = Revenue – Cost = 57650 – 81.20T – (370T – 0.56T^2) = 57650 – 81.20T – 370T + 0.56T^2 = 57650 - 451.20T + 0.56T^2 ……………….. (1)

Differentiating equation (1) with rest to T, equate to 0 and solve for T, we have:

P’ = –451.20 + 1.12T = 0

1.12T = 451.20

T = 451.20 / 1.12

T = 402.86

Therefore, the ticket price, T, that will maximize the airline's profit is $402.86.