1. (30 points) Remin sells chocolate on Hagwarts Express to fend off dementors. She uses the newsvendor model to order a special kind of white chocolate (in bars) every month. One bar costs $4 to the store. Any bars that are not sold at the end of a month, are included to a gift set for $2 per bar sold at Hog's Head. Remin knows that the probability density function of the demand for this special white chocolate is f (x) = 11:50, for a: E [0, 150] . Remin calculates that she needs to order 80 bars of this chocolate for the next month. Assume that she orders optimally. (a) (8 points) Find the selling price of one white chocolate bar. (b) (4 points) Why does Remin not use EOQ model? (c) (5 points] If the order purchase estimation was 150 bars, would the selling price be higher or lower? Explain without recalculating the selling price. ((1) (5 points) If the optimal order quantity estimation is 90 bars, the selling price is the same as in part (a) and the pdf of the demand is x) = arr, for .z E [013 ], could you conclude whether cu is larger or smaller than H2157) '3' Explain without calculating a. (e) (8 points) Assume that only at most 10 unsold bars can be included into gift sets, the rest of the unsold bars goes to charity ($0 per item). Derive the expected cost function. 2. {22 points) A puzzle store, Dorogi's Wizard Wheezes, has different variety of brainteasers and jigsaw puzzles. One particular puzzle, Impossible, sells for 525 each, and it costs $15 to purchase it from a designer. There is a 5550 replenishment cost per order. A backorder results in the loss-ofgoodwill with estimated cost 340 per puzzle. You can assume the unmet demand is backlogged. There is a 2-month lead time and an inventory carrying charge of 15 % annual interest rate. The monthly demand for Impmsible puzzle follows a normal distribution with mean 300 and standard deviation 65. (a) (4 points) What is the value of Q3, if Q5 is estimated using the EOQ model? (b) (4 points) What is the value of Ra? (c) [4 points) What are the values of Q1 and R1? ((1) (10 points) Currently Dorogi's uses the reorder point of 20 units and the lot size of 100 units. A manager from the new generation of puzzle masters, Natalia, plans to increase the lot size from 100 units to 120 units. Then, does the probability of not stocking out during the lead time increase or decrease? How about the proportion of demand that is met from onhand stock? Explain your reasoning clearly either with math or in words. 3. (28 points) During lunch time customers arrive at the Leaky Cauldron and order the world famous Liu cheesecake and do not leave without a treat. Arrivals are assumed to be Poisson in nature. The average time to choose a avor of the cheesecake and place the order is 2 minutes. The service times vary greatly depending on the specic order as master Zhenyuan needs to prepare the Special ingredient for each cake personally, so the process of serving the customer follows an exponential distribution. (a) (4 points) What are the arrival and service rates in minutes if an arrival rate is 4 customers every 5 min and there is one server? Can the queue reach a steady state? Why or why not
