$3)$ A production facility manufactures custom metal brackets using a batch production process. The company plans to adopt the Economic Production Quantity $($EPQ$)$ model to optimize its inventory replenishment. The production rate is significantly higher than the usage rate, allowing inventory to accumulate during production. Annual demand: $12,000$ units Setup cost per production run: $$200$ Holding cost per unit per year: $$4$ Daily production rate: $300$ units Daily usage rate: $100$ units Number of working days per year: $300($a$)$ Calculate the Economic Production Quantity $($EPQ$)$ and the maximum inventory level. Round both answers to the nearest whole number. $($b$)$ Draw a flowchart that shows the steps of the EPQ replenishment cycle, from setup decision to production, inventory accumulation, consumption, and reorder trigger.$($ Dont upload image draw the flowchart$)$