I. Le Meridien in San Francisco has 160 rooms. The hotel has an ample low fare demand at the room rate of 5200 per night, but the demand from the high fare class which pays $450 per night on average, is uncertain. The high fare demand is normally distributed with mean 60 and standard deviation 42. How many rooms should Le Meridien protect for high fare customers to maximize expected revenue? (Leave your answer in decimal form, i.e., no need to round to an integer value.) Suppose Le Meridien sets a booking limit of 100 for low fare customers. How many high fare customers does the hotel expect to turn away due to a lack of rooms? When high-fare demand is less than their protection level, the Le Meridien assumes rooms go empty because it is too late to sell the rooms to low-fare arrivals. But now they have an opportunity to sell those rooms at the last-minute to a third party seller of opaque goods (such as hotwire.com and price-line). The third party seller buys the room inventory on the day at $80, and assumes all the risk of selling those rooms on its website. What critical ratio should the hotel use for setting the protection level for its high fare customer class (who continue to pay $450 per night, and whose demand is still normally distributed with mean 60 and standard deviation 42) knowing that it now has this opportunity to sell off remaining inventory at the last minute for $80? (Early demand at the low fare of $200 remains ample and Le Meridien still makes this decision to maximize expected revenue.)