Question 1: [10 marks] Lingnan Bakery (LB) uses at a steady rate of 100 kilograms of butter to produce bread every day. The cost to order butter from a supplier is $50 per order and the annual holding costs of the butter is SH per kilogram. Consider LB operates 360 days per year. a. If LB orders 500 kilograms of butter each time and spends $5000 on ordering and holding the butter annually, show that the annual holding costs of the butter per kilogram H is $5.6 per kilogram per year. b. Will you advise LB to adopt the EOQ to order the butter? Justify your answer. Question 2: [15 marks] Reconsider question 1: Suppose LB can get the butter from a supplier with the following price scheme, determine the optimal order quantity in kilograms of butter and the optimal annual total cost. Weight in Kilograms 1 to 499 500 to 999 1000 or more Unit Price $10.0 [2 marks] [8 marks] $9.5 $8.0 Question 3: [12 marks] Lingnan Barkey (LB) sells egg tarts. Historically, LB has observed that hourly demand of egg tarts is normally distributed with a mean of 100 units and a standard deviation of 10 units. The baking time of egg tarts (lead time) appears normally distributed with a mean of 0.5 hours and a standard deviation of 0.1 hours. LB aims to limit the stock out risk during lead time to 10 percent. When should LB start to bake a new batch of egg tarts? Question 4: [13 marks] Lingnan Bakery (LB) also makes cream cakes. Cream cakes cost $75 each to make, and LB sells for $250 each. Every day, 2 hours before the bakery is closed, those unsold cream cakes are reduced to half-price of the regular price of $250 and typically 50% of those are sold. Any that unsold on the day are discarded. The daily demand of cream cakes can be approximated by a normal distribution with = 50 cakes ands = 5 cakes. a. What inventory model should be used to determine the quantity of cream cakes prepared daily in order to maximize the total expected daily profit? Why? [3 marks] b. What is the critical ratio (optimal service level)? [5 marks] c. How many cream cakes should be prepared daily to maximize the total daily expected profit of this product? [5 marks] End of Assignment 3