An automobile brake supplier operates on two 8-hour shifts, 5 days per week, 52 weeks per year. Table shows the time standards, lot sizes, and demand forecasts for three components. Because of demand uncertainties, the operations manager obtained three demand forecasts (pessimistic, expected, and optimistic). The manager believes that a 20 percent capacity cushion is best.

a. What is the minimum number of machines needed? The expected number? The maximum number?
b. If the operation currently has three machines and the manager is willing to expand capacity by 20 percent through short-term options in the event that the optimistic demand occurs, what is the capacitygap?

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CAPACITY INFORMATION FOR AUTOMOTIVE BRAKE SUPPLIER Time Standard Demand Forecast Componentrocesing (hrlunit Setup (hr/ot Lot Size (ntot) PessimisticExpected Optimistic A. 0.05 0.20 0.05 1.0 4.5 8.2 60 80 120 15,000 10,000 17.000 18,000 13,000 25,000 25,000 17,000 40,000