$30.$ The Yeasty Brewing Company produces a popular local beer known as Iron Stomach. eer sales are somewhat seasonal, and Yeasty is planning its production and workforce levels on March $31$ for the next six months. The demand forecasts are as follows: Production Days Forecasted Demand $($in hundreds of cases$)$ Month April May June July August September $20231620859312217614063$ As of March $31,$ Yeasty had $86$ workers on the payroll. Over a period of $26$ work$-$ ing days when there were $100$ workers on the payroll, Yeasty produced $12,000$ cases of beer. The cost to hire each worker is $$125$ and the cost of laying off each worker is $$300.$ Holding costs amount to $75$ cents per case per month. As of March $31,$ Yeasty expects to have $4,500$ cases of beer in stock, and it wants to maintain a minimum buffer inventory of $1,000$ cases each month. It plans to start October with $3,000$ cases on hand.