Problem 2 (16 points) - Formulating Production Planning Problem with Backlogging The demand for a particular product in the next four months is provided in the table on the right. Assume a fixed production capacity of 1000 units per month; Month the production cost is $10 per unit, storage cost is $1 per unit per month for each unsoldyanit held over, and backlogging cost is $5 per unit per month late. (Note: Jan "backigging" is when you don't meet the demand immediately, but it will cost Feb you to do so.) Formulate an IP to determine a production plan that minimizes Mar total cost. Assume zero initial inventory, zero closing inventory, zero initial backlogs, and zero closing backlogs. Clearly define the decision variables, Apr parameters (if used), objective function, and constraints. Units Demanded 800 900 1100 700