I recommend opening the west wing year round as only a 2% occupancy rate would justify doing this. I would hold off on building the pool as it is a major capital expenditure and makes it much riskier that it will breakeven on the investment. Moreover, it is not entirely clear what effect the pool will have on the occupancy rate. Therefore, since it is very likely the hotel can maintain 2% occupancy rates during the off-season, and likely much more than that, this is the best and most profitable choice.
The profit margin of the hotel (profit as a percent of sales) is $11k/160k = 7%. However, if they decide to open the hotel for the summer they would need to reach 24% occupancy in order to reach the same absolute profits of about $11k and their profit margin would drop to 6%. The only way they can maintain profit margins of 7 to 7.5% would be to get occupancy during the off-season of 30%, which is definitely not a sure thing. One option would be to try opening the hotel for the off-season for one-year and testing what occupancy rates they can expect. If they are lower than they need, they could always decide not to open the hotel during the off-season in the future. This option does not exist for the “pool” options. Once they decide to build a pool they will have incurred a major capital expenditure and will likely need to support this investment over time in order to please their clientele who might have gotten used to having a pool. Therefore, while the business is quite profitable as is, I would still choose to open the hotel in the summer months.