Alpha Airlines must decide how many meals to load on its daily 6 pm non-stop flight from Denver to San Francisco. The meals are sold on board to economy class passengers for $10.00 and cost the airline $4.00 each. All meal orders must be made at least 48 hours before the flight departs. Any meals left over at the end of the flight are tossed into the trash by the ground clean-up crew. If Alpha runs out of meals, they will give the customer two bags of peanuts for free, which costs Alpha a total of $1.00. Alpha estimates that the demand for meals on this flight is Poisson distributed with a mean of 9.
a. What are the underage and overage costs?
b. How many meals should Alpha order to maximize their profit?
c. Alpha has decided to use all leftover meals on its local flight from San Francisco to Sacramento. They have determined that the cost of re-stocking such meals from the Denver-San Francisco flight to the San Francisco-Sacramento flight is $2.50 per meal. Any extra meals used on the flight to Sacramento are sold for $5.00, and it’s assumed that all meals will be sold (no leftover meals on that flight). How many meals should Alpha order for its flight to San Francisco in this scenario?