Operations Strategies: Assignment 1 Problem Set Name: Problem 1: Motorola obtains cell phones from its contract manufacturer in China to serve the U.S. market. The U.S. market is served from a warehouse in Memphis, Tennessee. Daily demand at the Memphis warehouse is normally distributed, with a mean of 5000 and a standard deviation of 4000 . Demands on different days are independent from each other and identically distributed. Motorola uses sea transportation with a lead time of 36 days and a fixed cost of $50 per order. Assume 365 days in a year. Motorola uses a holding cost based on 20 percent annual interest rate. The manufacturer offers Motorola an incremental discount: while each phone costs $100 per unit, any units above 10,000 will be discounted to $95 per unit and any units above 15,000 will be discounted to $90 per unit. All other parameters remain the same. Ignoring demand variability, what is the optimal order quantity that minimizes the annual ordering, holding cost and purchasing costs? Problem 2: Hilton on Time Square, New York City, has 444 guest rooms. Hilton can sell all its hotel rooms at a discounted price of $260 per night to customers with a two-week advanced purchase. Hilton can also sell its hotel rooms at its full price of $380 per night to customers without advanced purchase. For any unsold hotel room, Hilton has a 75% chance of selling it to some bidder from priceline.com at \$120 per night on the day before. The number of customers who buy at full price without advanced purchase can be 100,200,300, or 400 , with equal probability. Answer the following questions. 1. What is the overage cost of a full-price room? 2. What is the underage cost of a full-price room? 3. How many rooms should Hilton reserve for the customers without advanced purchase? 4. What is the probability all full-price customers will get a room? 5 What ic the exnected fraction of full-nrice cuctnmerc whn ret a ronm