Q$10$: When high$-$fare demand is less than their protection level, The Warwick 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 or Priceline.com. The third$-$party seller buys the room inventory on the day at $$50$ and assumes all the risk of selling those rooms on its website. What critical ratio should the hotel use for setting the protection level for its high fare customer class $($who continue to pay $$330$ per night, and whose demand is still normally distributed with mean $50$ and standard deviation $30)$ knowing that it now has this opportunity to sell off remaining inventory at the last minute for $$50?$ Early demand at the low fare of $$150$ remains ample, and the Warwick still makes this decision to maximize expected revenue.