Q4) Consider a three months inventory planning problem. Each month's demand is given in the table below with their probabilities. The setup cost is $20, and the variable production cost is $5/unit. Holding cost is $2/unit and applied to the ending inventory of each month. At the end of month 3, after paying the holding cost any leftover product may be salvaged for $1/unit. Selling price of the product is $60/unit No shortages are allowed. Assume that the production capacity is 6 units, and storage capacity is 3 units. And the beginning of month 1, there is 1 unit of product. Your goal is to maximize the expected net profit over the next three months. 80% Month Demand Probability 2 units 60% 1 3 units 40% 1 unit 50% 2 2 units 50% 3 2 units 3 units 20% a) Write down how you define the stages, the states and the decisions clearly. Write down the recursion equation with all required constraints and necessary functions. Define all functions mathematically and using dynamic programming find the optimal production plan to maximize expected profit b) Write down the optimal production plan if month 1 demand is 2 units, month 2 demand is 1 unit and month 3 demand is 2 units