Determining the number of machines needed

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The King Company is producing two types of products: A and B. Both products are produced on the same machining operation. The machines operate on two 8-hour shifts, 5 days per week, and 50 weeks per year. The manager wants to maintain a 20 percent capacity cushion. The demand forecast, batch sizes, processing times, and setup times are given in the below table. What is the minimum number of machines needed to meet demand?

Product A Product B
Demand forecast (units/yr) 150,000 180,000
Batch size (units/batch) 100 40
Processing time (hr/unit) 0.3 0.15
Setup time (hr/batch) 1 1.2

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