5. (6 points) The American Airlines flight from Reagan National to Dallas-Fort-W

Question

5. (6 points) The American Airlines flight from Reagan National to Dallas-Fort-Worth has 200 economy seats. The airline would like to determine how many to sell as refundable tickets for a price of $500 and how many to sell as economy, non-refundable tickets for a price of $290. Demand is essentially unlimited for the economy tickets as Dallas-Fort Worth is an American hub. Demand for refundable tickets has been studied and has found to be normally distributed with a mean of 35 and a standard deviation of 10. How many tickets of each type, refundable and non-refundable, should American sell for this flight?

Explanation / Answer

D=demand of No: of refundable seats.

Q=Number of refundable seats actually alloted

If D>=Q, revenue loss=(D-Q)*(500-290) ie loss incurred not selling at $500 but selling at $290

=(D-Q)*210

unit cost of refundable seat shortage, Cu=210

If D<=Q, loss due to unused seats= (Q-D)*500

unit cost of excess seats, Co=500

area under curve=critical ratio=Cu/(Co+Cu)=210/(500+210)=0.2957

F(Q)=std dev*Z+mean

get the value of Z from standard normal table corresponding to area under the curve, z=-0.55

Q=35+10*(-0.55)

~30

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