I am stuck in section C. Please show a clear step-by-step solution. PLEASE USE THE NUMBER PROVIDED IN THIS TABLE AND NOT FROM OTHERS. YOU MAY HAVE TO WORK OUT THE FIRST ONE (A) TO GET TO C, WHICH IS WHAT I AM LOOKING FOR. THANKS!

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 20 percent capacity cushion is best. Q i Component A Time Standard Processing Setup (hr/unit) (hr/lot) 0.05 Demand Forecast Lot Size Pessimistic Expected (units/lot) 60 15,000 17,000 75 9,000 Optimistic 27,000 1.0 4.2 B 0.20 12,000 17,000 0.05 8.7 100 16,000 24,000 40,000 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.) Capacity Demand Forecast Requirement (M) Pessimistic 2 machines Expected 3 machines Optimistic 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 Requirement (M) Capacity 2 machines Pessimistic Expected 2 machines Optimistic 3 machines c. If the operations manager has three machines and believes that the plant can reduce setup time by 20 percent through process improvement initiatives, does that plant have adequate capacity to meet all demand scenarios without increasing lot sizes? (Enter your responses rounded up to the next whole number.) Demand Forecast Requirement (M) Capacity machines Pessimistic Expected machines Optimistic machines