A firm produces automobile fuel filters. Current demand is constant at 200 units per month. The firm can produce these filters at a rate of 50 filters per hour. Each setup costs the firm $232.50. The firm uses a 22% annual rate for holding inventory. The filters cost $2.50 to produce and they are sold for $5.50 each. Assume a 6-hour workday, 20 days per month, and 12 months per year. Find: a) The optimal number of filters to produce in each production run; b) the amount of 'uptime' each production cycle; c) what is the max dollar investment in filters at any point in time