5. [20 points] Demand for Company LMN for the next 12 months is given in the following table: Month January February March April May June July August September October Demand Forecast 2,400 3,000 3,000 3,500 6,000 8,000 8,500 8,700 5,200 4,000 5,000 7,500 November December Company LMN employs 20 workers and has 2,000 units in inventory on January 1. In addition, the following information defines the operations at Company LMN for the next 12 months: a. Material costs/unit = $12 b. Inventory holding cost/unit/month = $5 c. Marginal cost of stockout/unit/month = $8 d. Hiring and training cost/worker = $500 e. Layoff cost/worker = $1,500 f. Labor hours required/unit = 1.25 g. Regular time cost/hour = $12 2 h. Overtime cost/hour = $18 i. Marginal subcontracting cost/unit = $35 j. Revenue/unit = $42 k. Days worked/worker/month = 20 1. Hour worked/worker/day = 8 m. Maximum overtime hours/worker/month = 10 n. End of year inventory required = 2,000 Provide an aggregate plan to maximize profit over the next 12 months, and report the maximum profit.