So, in which month the stockout occured?

The Union Street Microbrewery makes Monon Mild beer, which it bottles and then sells in its adjoining restaurant. It costs $750 to set up to brew a batch of beer. The unit cost of brewing and bottling is $1.75 per bottle. It takes one month to brew, ferment and bottle the batch of beer before it is ready to be consumed. A bottle of Monon Mild sells for $5. The monthly cost to store the beer in inventory is $0.20 per bottle. This cost is incurred for the monthly ending inventory of ready-to-sell beer (after demand has been met). The shelf life of the beer is long enough that storage time is not a concern. The average monthly demand for beer is 2000 bottles, but it varies by a seasonal factor depending on the month as shown below. So, for example, the demand for February is 2000*.81 = 1620 bottles. Jan 0.78 Feb 0.81 Mar 0.85 Apr 1.03 May 1.11 Jun 1.2 Jul 1.22 Aug 1.3 Sep 1 Oct 0.96 Nov 0.94 Dec 0.8 At present, they start a new batch of Monon Mild when the end of the prior month inventory reaches 1000 bottles. (e.g. If they have 800 bottles left at the end of month 2, setup happens at the end of month 2, production happens throughout month 3 and the beer is ready for consumption at the start of month 4.) The brewery has the capacity to produce 3000 bottles per month. When a batch is made, they currently produce at full capacity. Any demand that cannot be met is lost. a) Develop a model that represents this scenario over a 12 month, January to December, period. The ending inventory in the month prior to January was 1800 bottles. (Note that no batch would be in process according to their present policy, but with a different policy, there could be. The setup cost for that batch would not be included in this 12 month time frame, although the production and holding costs would be.) For the year, report the total profit, the number of production runs, the maximum inventory level and the number of months in which a stockout occurred.