A beer distributor finds that it sells on average $100$ cases a week of regular $12-$oz$.$ Budweiser. For this problem assume that demand occurs at a constant rate over a $50$ week year. The distributor currently purchases beer every two weeks at a cost of $$12$ per case. The inventory$-$related holding cost $($capital$,$ insurance, etc.$)$ for the distributor equals $33$ percent of the dollar value of inventory per year. Each order placed with the supplier costs the distributor $$9.$ This cost includes labor, forms, postage, and so forth. $($c$)$ Assume the brewer is willing to give a $9$ percent quantity discount if the distributor orders $640$ cases or more at a time. If the distributor is interested in minimizing its total cost $($i$.$e$.,$ purchase and inventory$-$related costs$),$ should the distributor begin ordering $640$ or more cases at a time? $(2$pts$)$