A_ll calculations (including the nal answer) to 2 decimal places. To obtain full credit, please show all work leading to the nal answer. Question 1 The Supermarket Store is about to place an order for Halloween candy. One best-selling :brand of candy can be purchased at $ 2.50 per box before and up to Halloween. After Halloween, all the remaining candy can be marked down and sold for $ 1.00 per box. Assume that the loss in goodwill \"cost\" stemming from customers whose demand is not satised is $ 0.35. The store is considering a price per box of $ 4, $ 4.50, $ 5, and $ 5.50. Recognizing that demand is price dependent, through market research the store determines that demand distribution for these prices is as follows. Demand Distribution when Demand Distribution when Sales Price : $ 4.00 Sales Price : $ 4.50 80 0.05 Demand (boxes) Probability Demand (boxes) Probability 70 n n 0.1 100 0.2 110 140 Probability 0.05 You are required to assist the store manager in completing the table below. Sales Price Optimal Stocking Expected Prot Expected Shortage Quantit Q" inunits ES U Q" in $ ES Q* inunits $ 4.00 $ 5.00 $ 5.50 $4.50 Make sure to show all work leading to the summary answers in the table above. Question 2 Inn at Penn has 200 rooms. During the summer months, if the rooms are priced at the low-rate of $300 per night, the hotel can achieve full-occupancy. Recognizing that there might be business customers with a higher willingness to pay for these same rooms during the summer, the hotel manager is contemplating offering these rooms to such customers at three potential higher rates of $ 450, $ 550, and $ 650. However, the manager is also cognizant of the fact that demand at a higher rate will be uncertain and hence, through a market analysis obtains the following additional data: 1. For a high rate of $ 450, demand from business customers will be normally distributed with a mean of 100 with a standard deviation of 30; 2. For a high rate of $ 550, demand from business customers will be normally distributed with a mean of 90 with a standard deviation of 20; and 3. For a high rate of $ 650, demand from business customers will be normally distributed with a mean of 60 with a standard deviation of 15. You are required to assist the store manager in completing the table below. Protection Booking Expected Expected Expected Expected Daily Customers rooms total rooms Revenue turned away occupied occupied at high- (at high- rate rate and low-rate Remember to show all work leading to the nal answer. Question 3 On a given MCO-ATL ight, there are 200 seats and each seat is sold at an average ticket price of 300. It has been observed that on most days in the past month, the ight rarely approaches 100% occupancy since there are passenger no-shows. Hence, the airline decides to overbook ights. The airline manager assigned the task of determining the number of seats to overbook on this ight estimates: (a) no-shows using historical information; and (b) service denial rate the airline should offer if on a specific day a customer is denied a seat due to overbookings. However, she encounters an interesting conundrum: Both the mean and std. deviation of no-shows changes based on the service denial rate offered. This leads the manager to consider alternative overbooking strategies with each one corresponding to the possible different service denial rates. No-show data for each service denial rate are: 1. Service Denial Rate of $ 400 in this case, no-shows are normally distributed with a mean of 30 and standard deviation of 8. 2. Service Denial Rate of $ 450 in this case, no-shows are normally distributed with a mean of 25 and standard deviation of 6. 3. Service Denial Rate of $ 500 , in this case, no-shows are normally distributed with a mean of 20 and standard deviation of 4. You are required to assist the store manager in completing the table below. Optimal Percentage Expected Expected Overbooks of time loss ($) loss ($) customers through for empty will be bumping passengers Remember to show all work leading to the nal