Answer:
$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
