3. A special product is required at a constant rate of 6000 units per month. The company can produce it at a rate of 300 units per hour. The equipment must be set up for production. It takes 6 hours to do the set up. The labor cost including overhead is 30 USD/hour. Factory idle time during set up is estimated at 180 USD/hour in lost profit. Each product costs 6 USD to produce and sold at 9 USD/unit. Annual interest is 20% in determining the holding cost. The factory works 8 hours a day, 20 days per month and 12 months per year. a) Determine the optimal production batch size to minimize the total costs. b) Determine the optimum length of each production run. c) Determine the average holding and set up costs. d) What is the maximum level of on-hand inventory? e) What percent of the time the company produces this product?