An airline company operates a plane between ATL and DC. This plane has 120 seats

Question

An airline company operates a plane between ATL and DC. This plane has 120 seats for economy class with two price tiers: low fare at $250 and high fare at $420. The low fare seats target for travelers and there is an unlimited demand from travelers. So seats offered at $250 will always be sold out. The high fare seats target for business travelers and the company believes that the number of business travelers for this route follows Poisson with mean 20. As business travelers plan for their travels in the last minute, any seats assigned to business travelers must be remained and cannot be offered to travelers.

1). How many seats should be assigned to the business travelers to maximize the revenue?

2). Calculate the expected revenue when the company offers the optimal number of seats to business travelers.

Explanation / Answer

Since number of business travellers follows Poisson distribution, the optimal number of business travellers will be the mean of Poisson distribution i.e 20. In other words, the probability that there will be 20 business travellers will be highest among all other numbers. So to maximize the revenue we must assign 20 seats to business travellers.
1) 20

2) Expected revenue when company offers 20 seats to business travellers
Out of 120 seats, 100 seats will be offered to Economy travellers for $250 each, and 20 seats will be offered to business travellers for $420 each. Hence Expected revenue: (100 x 250) + (20 x 420)
= $33, 400

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