During the past tourist season, Surfside Hotel did not achieve very high occupancy despite a reservation system that was designed to keep the hotel fully booked. Apparently, prospective guests were making reservations that, for one reason or another, they failed to honor. A review of front-desk records during the current peak period, when the hotel was fully booked, revealed the record of no-shows given in the following table. There is a $200 opportunity loss from a no-show. The resulting loss when a guest is overbooked is also $100. Surfside currently overbooks for 2 rooms. Should Surfside revise its booking policy?

(PLEASE SOLVE WITH FORMULA METHOD, NOT the cost matrix method, then compare with the cumulative probabilities to determine how many rooms they should overbook.)

(Does Cu = $100 and Co = $200 or vice versa?)

\begin{tabular}{c|cc} No-shows & Probability & cumulative Probability \\ \hline 0 & 0.06 & 0.06 \\ 1 & 0.1 & 0.1 + 0.06 = 0.16 \\ 2 & 0.16 & 0.16 + 0.16 = 0.32 \\ 3 & 0.3 & 0.3 + 0.32 = 0.62 \\ 4 & 0.14 & 0.14 + 0.62 = 0.76 \\ 5 & 0.07 & 0.07 + 0.76 = 0.83 \\ 6 & 0.06 & 0.06 + 0.83 = 0.89 \\ 7 & 0.06 & 0.06 + 0.89 = 0.95 \\ 8 & 0.05 & 0.95 + 0.05 = 1.00 \end{tabular}