For graduation, a hotel near the university always fills up. The average room rate is $80. When the hotel is overbooked, the policy is to find a room at a nearby hotel and pay for the room for the customer. This usually costs the hotel $200 since last minute rooms are expensive. History shows that the following probabilities of last-minute cancelations are likely: (5 points) a. What is the cost of underestimating demand? b. What is the cost of overestimating demand? c. Calculate the P(Q) or probability of the optimal order quantity =Cu/(Cu+Cs) d. How many overbookings (extra reservations) should the hotel take to minimize the total cost given the information above? Show your work