Problem $3$: $20$ points

A local store $($ToolsAreUs$)$ carries a popular power drill that is imported from Japan. Because of where the drill is produced, there is a long lead$-$time of $6$ months for this product. The lead$-$time demand is Normally distributed with a mean of $500$ units and a standard deviation of $100$ units. The drill costs ToolsAreUs $$30/$unit and they use a $35\%$ interest rate to estimate holding cost$/$unit$/$year$.$ Ordering and shipping costs$/$order are estimated to be $$750.$ The long delivery lead$-$time causes the ToolsAreUs to frequently not have the product on hand when a customer needs it$.$ ToolsAreUs knows that is costly to them to not have the item for immediate delivery to their customers. They have decided that a $(Q,R)$ inventory policy makes the most sense for this random demand situation, but they really have no idea how to estimate the penalty cost of a late item. So$,$ ToolsAreUs has decided that they want at least $98\%$ of the orders to be filled from stock, that is they want no more than $2\%$ of each order quantity to be delayed $($back$-$ordered$).$ Their manufacturing engineering intern calls this "Type $2$ service" based on her MANE $4331$ coursework. What are the $(Q,R)$ values to be used for ordering this drill? Hint: Use the EOQ as Q $,$ to find Q$0,$ R$0,$ and attempt a second iterations, i$.$e$.$ do an iteration to find Q$1$ and R$1.$