Question

2. If an airlines’ demand function in a specific market is:

D=-8*P+100*F+1000,

Where:

D represents the total number of passengers;

P represented the average price charged to passengers ($);

F represents the daily service frequency in that market.

And the cost function is:

C=800*F+3*D+100,000

Where:

C represents the total cost ($);

F and D are the same as defined above.

1) If the airlines’ daily service frequency is fixed at 15; the airlines can charge $100, $150, $185 and $200 to passengers, which ticket price will give airlines maximum traffic? maximum revenue? least cost? maximum profit?

2) If the airlines’ ticket price is fixed at $185; the airlines can provide service 10, 12, 15 or 18 times per day, which service frequency will give airlines maximum traffic? maximum revenue? least cost? maximum profit?

3) If the airlines can charge $150 or $185, and can fly 12 or 15 times per day, which combination of the price and frequency will give the airlines maximum traffic?

Answer 1

(1) Total revenue (TR) = P x D and Profit = TR - TC

We construct following data table.

F	P ($)	D	TR ($) = D x P	TC ($)	Profit ($) = TR - TC
15	100	1,700	1,70,000	1,06,600	63,400
15	150	1,300	1,95,000	1,05,400	89,600
15	184	1,028	1,89,152	1,04,584	84,568
15	200	900	1,80,000	1,04,200	75,800

(i) Maximum traffic (D) (= 1,700) when P = $100

(ii) Maximum revenue (= $195,000) when P = $150

(iii) Least cost (= $104,200) when P = $200

(iv) Maximum profit (= $89,600) when P = $150

(2)

We construct following data table.

F	P ($)	D	TR ($) = D x P	TC ($)	Profit ($) = TR - TC
10	185	520	96,200	1,02,560	-6,360
12	185	720	1,33,200	1,03,360	29,840
15	185	1,020	1,88,700	1,04,560	84,140
18	185	1,320	2,44,200	1,05,760	1,38,440

(i) Maximum traffic (D) (= 1,320) when F = 18

(ii) Maximum revenue (= $244,200) when F = 18

(iii) Least cost (= $102,560) when F = 10

(iv) Maximum profit (= $138,440) when F = 18

(2)

We construct following data table.

F	P ($)	D	TR ($) = D x P	TC ($)	Profit ($) = TR - TC
12	150	1,000	1,50,000	1,04,200	45,800
12	185	720	1,33,200	1,03,360	29,840
15	150	1,300	1,95,000	1,05,400	89,600
15	185	1,020	1,88,700	1,04,560	84,140

Maximum traffic (D) (= 1,300) when P = $150 and F = 15.