Macon Controls produces three different types of control units used to protect industrial equipment from overheating. Each of these units must be processed by a machine that Macon considers to be their process bottleneck. The plant operates on two 8-hour shifts, 5 days per week, 52 weeks per year. The table below provides the time standards at the bottleneck, lot sizes, and demand forecasts for the three units. Because of demand uncertainties, the operations manager obtained three demand forecasts (pessimistic, expected, and optimistic). The manager believes that a 30 percent capacity cushion is best. Time Standard Processing Demand Forecast Setup Lot Size Component Pessimistic Expected Optimistic (hr/unit) (hr/lot) (units/lot) A 0.04 1.0 60 16,000 16,000 B 0.20 C 0.05 4.1 8.7 75 12,000 100 27,000 17,000 35,000 9,000 17,000 23,000 a. How many machines are required to meet minimum (Pessimistic) demand, expected demand, and maximum (Optimistic) demand? (Enter your responses rounded up to the next whole number.) Demand Forecast Capacity Requirement (M) Pessimistic Expected Optimistic 2 machines 3 machines 4 machines b. How many machines are required if the operations manager decides to double lot sizes? (Enter your responses rounded up to the next whole number.) Demand Forecast Pessimistic Capacity Requirement (M) machines Expected machines Optimistic machines