Cumulative d Probability f(d) Probability F(d)
40 0.01 0.01
41 0.03 0.04
42 0.04 0.08
43 0.05 0.13
44 0.08 0.21
45 0.09 0.30
46 0.12 0.42
47 0.13 0.95
(In-Flight Meals) Oceanic Airlines sells meals aboard their flights. Obviously, the airline must decide how many meals to put on the airplane before the flight takes off, and it cannot restock additional meals if it runs out during the flight. Each meal sells for $7 and costs the airline $2.50. If there are meals left over at the end of the flight, the perishable items must be thrown away, but nonperishable items (crackers, napkins, etc.) may be reused. The value of the reusable items is estimated at $1.50. Assume there are no loss-of-goodwill penalties for unmet demand, only the lost profit.
a) Suppose the demand for meals on today's flight #815 has the distribution given How many meals should Oceanic stock on the flight?
b) Suppose instead that the demand for meals on flight #815 has a normal distribution with mean 50 and standard deviation 10. Now how many meals should Oceanic stock?
c) Calculate the optimal expected profit for meals sold on flight #815, still assuming demands are N(50, 102).