For a particular flight from Dulles to SF, USAir uses wide-body jets with a capacity of 430 passengers. It costs the airline $4,000 plus $60 per passenger to operate each flight. Through experience, USAir has discovered that if a ticket price is T, then they can expect (430 - 0.58T) passengers to book the flight. Determine the ticket price, T, that will maximize the airline's profit.

$370.69

Explanation:

Given the following :

Capacity (n) = 430

Cost incurred by airline per flight = $4000 + $60 per passengers

If ticket price = T ; (430 - 0.58T) are expected to book.

Determine the ticket price, T, that will maximize the airline's profit.

Profit = Revenue earned - cost incurred

Revenue earned = capacity * price = nT

Cost incurred = $4000 + $60n

Profit = nT - (4000 + 60n)

If ticket price = T ; (430 - 0.58T) are expected to book. Then n = (430 - 0.58T)

Profit = (430 - 0.58T)T - ($4000 + 60(430 - 0.58T))

Profit = 430T - 0.58T^2 - ($4000 + 25800 - 34.8)

Profit = 430T - 0.58T^2 - 4000 - 25800 + 34.8

Profit (P) = - 0.58T^2 + 430T −29834.8

Taking the first derivative of P

P' = 2(-0.58T) + 430

P' = - 1.16T + 430

Hence solve for price (T) when P' = 0

0 = - 1.16T + 430

1.16T = 430

T = 430 / 1.16

T = 370.68965

Price = $370.69