A machine center handles four types of clients: A, B. C, and D. The manager wants to assess the number of machines required to produce goods for these clients. Setup times for changeover from one client to another are negligible. Annual demand and processing times are uncertain: demand may be low, normal, or high. The probabilities for these three events arc shown in the following tables:

a. Explain how simulation could be used to generate a probability distribution for the total number of machine-hours required per year to serve the clients.
b. Simulate one year, using the following random numbers. Use random number 88 for client As demand, 24 for client A€™s processing time, and so forth.
88, 24, 33, 29, 52, 84, 37,92

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Client A Demand (units/yr) Probability Processing Time (hr/unit)Probability 0.10 0.60 0.30 10 20 30 0.35 0.45 0.20 3,000 4,200 Client B Demand (units/yr)Probability Processing Time (hr/unit)Probability 0.30 0.50 0.20 60 90 100 0.25 0.50 0.25 800 900 Client C Demand (units/yn) Probability Time Probability (hr/unit)Probability 1,500 3,000 4,500 0.10 0.50 0.40 12 15 20 0.25 0.60 0.15 Client D Demand (units/yr)Probability Processing Time (hr/unit) Probability 650 700 0.40 0.50 0.10 60 70 80 0.30 0.65 0.05