Let'curosity Brewing has been selling handmade, organic, small batches of beer in the village. They have seen a decrease in demand as a result of an ongoing pandemic and they are concerned about how to adjust production levels accordingly. In order to make sure that no bottles are wasted, Layla has been assigned with the task of developing a model for optimal batch size based on the expected sales figures for next month, which is projected at $30 \/bottle$ per unit sold. The cost to produce one batch (12 oz) is estimated at $50 and there are 15 bottles in each case. In addition, they have a contractual obligation of delivering not less than 8,000 cases but no more than 9,000 as well. How many barrels of beer should Younnios make to minimize the costs associated with producing too much and also satisfy the order demand?