Hanson Cooling Solutions (HCS) sells and services several brands of major air conditioners, including, window, portable and split ACs. Past sales for a particular portable model (PM-HC2) of air conditioner have resulted in the following probability distribution for demand: Demand Per Week Probability 0 0.05 1 0.23 2 0.28 3 0.16 0.13 0.15 4 5 The reorder lead time refers to the time (in weeks) between placing with and receiving from the manufacturer an order for new refrigerators. This lead time is described by the following distribution: Probability Lead Time (Week/s) 1 0.63 2 0.24 3 0.13 Based on the cost considerations as well as storage space, the company has decided to order 12 of these each time an order is placed. The holding cost(or inventory carrying cost) is $8 per week for each unit that is left in inventory at the end of the week. The stockout cost (or shortage cost) has been set at $47 per stockout (or unit of shortage). The company has decided to place an order whenever there are four or less air conditioners left at the end of the week. They cannot place an order unless they have received the previous order. Orders are received at the beginning of the week. If demand is fulfilled then it is considered to be sales, otherwise it is lost sales (i.e., a stockout). Shortage or Stockout: Demand that cannot be supplied from inventory. For example, if you have 2 units in stocks and demand is 4 units then you can only supply 2 units and the remaining 2 units are considered as stockout or lost sales. Lead time: The time between the placing of an order and its receipt in the inventory system. For example, if you place an order with the manufacturer at the end of week 4 and the lead time is 2 weeks then you are going to receive this order at the beginning of the week7. Meanwhile during weeks 5 and 6 you cannot place a new order. Simulate 12 weeks of operation for Hanson Cooling Solutions assuming there are currently 5 units of the portable model (PM-HC2) of air conditioners in inventory. Use as many as you need from the following set of random numbers: Random Numbers 0.85 0.81 0.56 0.91 0.88 0.54 0.93 0.71 0.72 0.68 0.96 0.79 0.14 0.48 for DEMAND Random Numbers 059 0.37 0.76 0.92 0.13 0.23 0.29 0.63 0.98 0.21 0.57 0.45 0.35 0.15 for LEAD TIME (a) Specify an appropriate random number mapping for the demand and lead time. (b) Use the given random numbers to simulate twelve weeks demand, in the given table, add as many rows as you need: [Note: must use the table below and fill it completely] S # Ordered units Received Beginning Ending Lost Lead Inventory Random Demand Inventory Sales Order? Random Time # Yes/No # After completion of 12 weeks' simulation answer the next 8 questions: (c) What is the total stockout (or shortage) cost? (d) What is the total inventory carrying cost? (e) How many times was an order placed? (f) In which week/s did they have the maximum number of air conditioners in ending inventory? (g) How many units of air conditioners were sold? (h) In which week did Hanson Cooling Solutions face highest $ amount in the lost sales or stockout? (i) In which week/s ending inventory of air conditioner in stock is greater than six units? In these 12 simulations, what is the percentage of stockout?