Please write down objective function formula and all constraints.

1. My dog Molly runs a biscuit manufacturing plant. The demand, production cost, holding cost, and production capacity vary from month to month. The data for the next year are given in the table below. Month Demand (in cases) Holding Cost (in S/case) Production Cost (in S/case) 6 6 50 Production Capacity in cases) 70 50 30 40 50 45 OCO NOUAWN - WWNNWWW AWN 40 50 60 80 60 45 80 60 50 20 11 3 5 6 30 40 To facilitate the formulation of a model, make the following assumptions: The holding costs are calculated on the amount of inventory (leftover cases) remaining at the end of the month (after demand has been met). There is no initial inventory at the beginning of the first month. There are no holding costs for the newly-produced cases which are delivered in a given month. That is, if 10 cases of biscuits are produced in month three and delivered in month three, then there is no holding cost to keep those cases. Holding costs are only charged on units held over from a previous month (or alternatively, those units carried over to the next month). Molly requires that the demand be met every month. Molly's task is to minimize the total production and inventory-holding costs over this twelve- month planning horizon. What is the optimal production and holding schedule? Give your answer in a clearly labeled table. What is the optimal cost? 2. Now omit the final assumption and instead assume that the demand doesn't have to be met every month, but if it's not, there is a penalty. In months 1-6, there is a $9/case penalty for any deficit between what is demanded and what is delivered in a given month, and for months 7-12, there is a $12/case penalty. Now what is the optimal production, holding and delivery/selling schedule? Give your answer in a clearly labeled table. What is the optimal cost