Question

NorthStar Airlines runs daily flights from Halifax to Montreal. The planes hold 60 passengers and cater to the business traveller with comparable business rates. The recent economic downturn has reduced the occupancy rate of flights to such an extent that NorthStar would like to offer a set number of seats at discount rates to gain more passengers. The board of directors is worried that discounted seats will cut into profit margins and will upset the regular business traveller. The ticket price for a business traveller is $350. Discounted tickets would sell for $120. Assuming that empty seats can be sold if discounted, use the following data gathered from 100 flights to determine how many seats should be discounted.

# of full fare passengers	Frequency
10	15
20	25
30	25
40	20
50	10
60	5

Answer 1

Plane capacity = 60

Business ticket price of full fare, f = $ 350

Discounted ticket price, d = $ 120

Critical ratio = (f-d)/f

= (350-120)/350

= 0.6571

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Cumulative probability distribution of full fare demand

# of full fare passengers	Frequency	Cumulative probability
10	15	0.15
20	25	0.4
30	25	0.65
40	20	0.85
50	10	0.95
60	5	1

In the above table, look for cumulative probability >= critical ratio (0.6571)

The corresponding # of full fare passengers is 40

Number of seats to be reserved for business travelers = 40

Number of seats to be discounted = 60 - 40

= 20

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ANSWER : 20