Read the case up to the $$Assignment$$ section. Then, use the following information $($and not theremaining information in the case$)$ to complete the case analysis:Forecast for next $12$ months:Month $123456789101112$ForecastedDemand$6007501000850750700750650800700750700$The plant shuts down for $2$ weeks in August $($this capacity is lost each year$),$ and all of the direct workerstake vacation during the closure. The regular$-$time rate for workers is $$10/$hour$,$ and overtime is paid attime and a half.The production manager said there were currently $50$ units in inventory. He also said that currentlyeach worker produces an average of $25$ pumps in any given month. There are currently $20$ workers inthe medium$-$size pump area$\mathrm{.}1.$ Develop three unique $($i$.$e$.,$ distinctly different$)$ Sales & Operations plans and include all relevantcosts based on the information provided in the case. The decision regarding ending inventory isa managerial decision. You should determine the desired ending inventory, and justify yourdecision, for each plan$\mathrm{.}2.$ Which plan would you choose or recommend? Are there pros and cons beyond cost which youconsidered in your decision? What were they, and why were you concerned?