Question $2[10$ marks$]$

A $500-$room hotel had an $80\%$ occupancy last night and expects $50\%$ of those guests to depart today. Historically, under stays are $7\%$ and overstays are $4\%.$ Reservations for the day appear to be $225$ guaranteed. Cancellations are $10$ for the guaranteed reservations. No shows are $40\%$ from the guaranteed bookings. Walk$-$in guests are historically $10.$ There are $5$ rooms out$-$of$-$order.

Calculate the number of rooms availability forecast with the following statistics given.

All workings must be s