Question 1 (a) Consider the "newsboy problem". The newspaper vendor ordered 100 newspapers from the supplier in anticipation of demand for newspapers the next day. The newsvendor calculated the expected profit to be $150. Later, the newsvendor computed the critical ratio for the problem as 0.57. The probabilities of possible demand of the newspaper are shown in Table 1. Analyse whether the quantity the newsvendor ordered is the best quantity to maximise the expected profit. Demand Table 1: Newspaper demand distribution 25 50 75 100 125 150 Probability 0.10 0.15 0.20 0.30 0.15 0.10 (9 marks) (b) The average weekly demand for a piece of respiratory equipment was found to be 25 units with a lead time of 3 weeks. The standard deviation of lead time demand is known to be 10 units. The company plans to provide a service level that is 47.7% more than the mean lead time demand. Both demand and lead time follow a normal distribution. The company determined that an order of 250 units is the optimal order quantity for the item. (i) Identify the ordering policy for the item. (ii) If the company decides not to keep any safety stock, what service level can it achieve? Question 2 Demand for video projectors from a reputed company over the last two years is shown in Table 2. The company is trying to forecast the demand for the year of 2022. Table 2: Monthly Demand for Video Projectors Month Demand Month Demand Jan-20 120 Jan-21 118 Feb-20 105 Feb-21 110 Mar-20 97 Mar-21 95 Apr-20 85 Apr-21 90 May-20 98 May-21 100 Jun-20 110 Jun-21 115 Jul-20 125 Jul-21 122 Aug-20 102 Aug-21 98 Sep-20 92 Sep-21 88 Oct-20 90 Oct-21 79 Nov-20 100 Nov-21 95 Dec-20 115 Dec-21 110 (a) Plot the demand data and comment on the pattern. What should be the most appropriate method to forecast demand for 2022? (6 marks) (b) The supply chain manager believes there is a linear relationship between demand and time and decides to use a regression analysis method to forecast the demand. Determine the regression equation for the given data. Clearly identify the dependent variable, independent variable, slope and intercept. Discuss whether regression analysis is appropriate or not to forecast demand in this situation. Provide your reasons. (c) The actual demand for the months of Jan-22 to Apr-22 were found to be 120, 100, 80 and 75, respectively. Compute the mean absolute deviation (MAD) based on the demand forecasts for 2022 using the method in part (b).