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Profit Maximization for American Airlines

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American Airlines leases a 300-seat carrier to fly its daily Dallas-Denver route. It recently lowered its ticket price from $240 to $200, and observed the following demand for seats by business and tourist-class passengers:

Price Q(business) Q(tourists) Q(total) Revenue (business) Revenue (tourists) Revenue (total)
240 90 10
200 130 50

The daily fixed costs of leasing aircrafts are as follows:
300 seats $32,000
260 seats $28,000
180 seats $20,000
American's service cost is $20 per passenger, regardless of the aircraft used.

1. Complete the chart.

2. How many passengers should American seek to carry on each flight to maximize
(i) its revenues?
(ii) its profits?

3. What prices should American charge if it is restricted to leasing 180-seat aircraft only?

4. What is the maximum profit will it make under the conditions in (2) above?

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Solution Preview

1. See the attached file.

2. First, find American's total Demand curve.

Slope of Demand curve:
When P = 240, Q(total) = 100. When P = 200, Q = 180.
Slope = rise/run
Slope = -40/80
Slope = -0.5

y-intercept of Demand curve:
P = -0.5Q + b
240 = -0.5(100) + b
b = 290

Function of ...

Solution Summary

Given price and quantity data for American Airlines, this solution shows how to maximize AA's revenues and profits for two different sizes of plane.