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Question 3 A Herr Cutter has run his barber shop from the same location for nearly 25 years. He opens his shop at 8.00 am each week day morning. He enjoys the relaxed working environment, the regular hours and the opportunity to visit with his customers. Over the years he has built a reliable clientele. He is a fine barber who takes pride in his work. He has observed however that in recent years his new customers are much less like to return as in early years. He attributes this to decreasing tolerance for waiting. He is considering whether to hire an assistant. He has been able to collect data on arrivals and service times over a number of days, and figures are summarized below. Time Between Arrivals (mins) Probability 0.2 Service Time (mins) 15 0.3 20 0.35 0.35 25 0.35 Probability 20 25 30 35 0.3 0.15 Required a) Construct the appropriate random number mappings for the random variables starting from 00 . (3 marks) b) Simulate 10 customers arriving at the using the random numbers given below. (12 marks) c) What is the average time a customer waits for service? (1 mark) d) What is the average time a customer is in the system (wait plus service time) (2 marks) e) What is the percent of time Cutter is busy with customers? (2 marks) Random Numbers To Be Used in the Simulation Customer 1 2 3 4 5 6 7 8 9 10 Interarrival time 0.08 0.87 0.15 0.04 0.52 0.46 0.96 0.10 0.02 0.76 Service Time 0.46 0.96 0.00 0.27 0.73 0.76 0.25 0.11 0.47 0.72 Use the following headings to complete the simulation Time Customer RN Between Arrival Begin Arrivals Customer RN Time Wait for Service service Time Between Arrival Begin Wait for Arrivals Time Service service RN RN Service End Time in Time Service System Service End Time in Time Service System Question 3B CWD Electronics sells computers , which it orders from the USA. Because of shipping and handling costs, each order must be for 12 units . Because of the time it takes to receive an order, the company places an order every time the present stock drops to 6 units. It costs $120 to place an order. It costs the company $75 in lost sales when a customer asks for a computer and the warehouse is out of stock. It costs $5 to keep each computer stored in the warehouse. If a customer cannot purchase a computer when it is requested, the customer will not wait until one comes in but will go to a competitor. The demand for computers and the time required to receive an order once it is placed (lead time) has the following probability distribution: Lead time (weeks) Probability Demand/ week Probability 2 0.20 0 0.10 3 0.65 1 0.45 4 0.15 2 0.30 0.15 The company has 10 computers in stock. Orders are always received at the beginning of the week. Note that a lead time of 2 weeks imply that an order placed at the end of week one will arrive at the beginning of week 4. Required a) Construct the appropriate random number mappings for the random variables starting with .00. (2.5 marks for demand and 1.5 mark for lead time) b) Simulate CWD's ordering and sales policy for 15 weeks. (12 marks) c) Compute the average cost of the policy( 4 marks) demand .49 .67 .06 .30 .95 .01 lead time .84 .79 .35 .56 .64 .21 .10 .70 .80 .66 .69 .76 .86 .56 .84 Use the following headings Week OI U R A I RN D D F EI SO order RN leadtime SOC OC TC IC