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

in 2001, dell computer became the world’s largest personal computer vendor, continuing to

gain market share and post profits in an industry struggling with slumping sales and billions of

dollars in losses. dell sells 90% of its pcs directly to the final customer, largely bypassing the

reseller channel that accounts for most of the world’s pc sales. this direct customer relationship

is the key to dell’s business model, and provides distinct advantages over the indirect sales

model. dell’s direct relationship with the customer allows it to tailor its offerings to customer

needs, offer add-on products and services, and use the internet to offer a variety of customer

services. in addition, dell’s pcs are built to customers’ specifications upon receipt of an order,

giving dell additional advantages over indirect pc vendors who must try to forecast demand and

ship products based on those forecasts. dell’s direct sales and build-to-order model has achieved

superior performance in the pc industry in terms of inventory turnover, reduced overhead, cash

conversion, and return on investment (kraemer, et al., 2000).

explanation:

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