In the coach (i.e., cheap) seats on airline flights theres no real food given out for free anymore, but most airlines will sell you something on board. Lets say the only choice is a mystery sandwich (See Fig. 1) selling for

$8.00, and that historically about 17% of passengers will opt to buy one (nobody buys more than one, and the other approximately 83% of passengers dont buy any).

Operationally, this means that each passenger on a flight has an independent probability of 0.17 of buying a sandwich, as if each passenger flips a biased coin with P(heads) = 0.17 and if it comes up heads this passenger buys a sandwich, and if it comes up tails this passenger does not buy a sandwich. The wholesale cost to the airline per sandwich is $4.75. If a passenger wants to buy a sandwich but theyre sold out by the time he or she is asked, then the airline incurs a loss-of-goodwill cost of

$10.00 for that hungry and disgruntled passenger. Any

unsold sandwiches left over have to be thrown out (so the airline gets no revenue, not even scrap/salvage, on any unsold sandwiches, and just loses the $4.75 on each one). Throughout, assume that all seats on a flight are occupied (which is almost true these days anyway). Well consider two types of airplanes, and composed completely of coach seats: the Embraer ERJ 135 a small regional jet with 37 seats, and the Airbus A380), currently the worlds largest commercial passenger jet with an all-coach-configuration capacity of 853 seats.

1. Determine how many sandwiches to put on a given flight to maximize the profit for the Embraer ERJ 135 in order to maximize the profit;

2. Determine how many sandwiches to put on a given flight to maximize the profit for the Airbus A380 in order to maximize the profit.