12. value 5.00 points Problem 13-43 Offwego Airlines has a daily flight from Chi

Question

12. value 5.00 points Problem 13-43 Offwego Airlines has a daily flight from Chicago to Las Vegas. On average, 14 ticket holders cancel their reservations, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a mean of 14 passengers and a standard deviation of 4.60 passengers. Profit per passenger is $92. If a passenger arrives but cannot board due to overbooking, the company policy is to provide a cash payment of $192 Use Table B. How many tickets should be overbooked to maximize expected profit? (Round your z value to 2 decimal places. Round your other intermediate calculations to 4 decimal places and final answer to the nearest whole number.) Overbooked tickets References eBook & Resources Difficulty: 2 Medium

Explanation / Answer

In the given case,

Underage cost = Cu = profit per passenger = $92

Overage cost = Co = cash payment per passenger = $ 192

Thus , Critical ratio = Cu / Cu + Co = 92 / ( 92 + 192) = 92 / 284 = 0.3239

Corresponding Z value for above Critical Ratio = NORMSINV ( 0.3239) = - 0.45682( - 0.46 ROUNDED TO 2 DECIMAL PLACES )

Thus, number of tickets to be overbooked

= Mean value of cancellation + Z x Standard deviation of cancellation

= 14 - 0.46 x 4.6

= 14 - 2.116

= 11. 884 ( 12 rounded to nearest whole number )

OVERBOOKED = 12 TICKETS

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