Jim Johnson Operates a Bus Service to Take College Students

Essay

Jim Johnson operates a bus service to take college students to "The Big City" on Friday night and bring them back to school on Sunday night. The bus has 45 seats but sometimes there are empty seats. His records show that about 5% of ticket holders do not show up for their ride. Tickets cost $20 and are non-refundable. If Jim overbooks the bus and more than 45 passengers show up, some of them will be bumped and have to miss the trip. This bumping costs the company $40 because Jim has a double-your-money back policy for bumped passengers. Jim plans to accept 48 reservations (overbook 3 seats).
$\begin{array}{|c|c|l|c|}\hline & \text { A } &{\text { B }} & \text { C } \\\hline 1 & &{\text { Jim's Big City Bus }} & \\\hline 2 & & \text { Reservation System } & \\\hline 3 & & & \\\hline 4 & & \text { Seats Available } & 45 \\\hline 5 & & \text { Ticket Price per Seat } & \$ 20 \\\hline 6 & & \text { Prob. of No-Show } & 0.05 \\\hline 7 & & \text { Cost of Bumping } & \$ 40 \\\hline 8 & & \text { Reservations Accepted } & 48 \\\hline 9 & & & \\\hline 10 & & \text { Passengers to Board } & 47 \\\hline 11 & & & \$ 960 \\\hline 12 & & \text { Ticket Revenue } & 0 \\\hline 13 & & \text { Opp. Cost of Empty Seats } & \$ 80 \\\hline 14 & & \text { Cost of Bumping Passengers } & \$ 880 \\\hline 15 & & \text { Marginal Profit } & \\\hline\end{array}$
What is Jim Johnson's expected marginal profit?