Consultant Air focuses business on high-paying McKinsey consultants, but to fill

Question

Consultant Air focuses business on high-paying McKinsey consultants, but to fill planes, it also carries the general public. It is flying a 100-seat jet from Atlanta to San Francisco and the consultant demand is normally distributed with mean 60 and standard deviation 10. Consultants pay $1,200 per ticket, the general public pays $150. Of course, the general public must book a flight several weeks ahead of time, while the consultants book flights at the last minute. Because the price is so cheap, the general public will take all the available seats not reserved for the consultants. How many seats should be opened up for the general public?

Explanation / Answer

First find number to reserve for consultant and let it be Q.

D=Demand for consultant

If D < Q; Overage Cost, earned nothing on Q - D, could've sold to low-fare so Co=$150.

IUnderage Cost; loss of high-fare,

Cu=$1200-$150=$1050.

CR=Cu/(Co+Cu)=0.875.

Z-score for probability 0.875=1.15.

Q=60+1.15*10=71.5 = 72 seats reserved for consultants.

General Public Booking Limit = 100-Q = 100-72=28 seats should be open for general public

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