Bobbi$$s Restaurant in Boise, Idaho, is a popular place for weekend brunch. The restaurant serves real maple syrup with French toast and pancakes. Bobbi buys the maple syrup from a company in Maine that requires three weeks for delivery. The syrup costs Bobbi $$4$ a bottle and may be purchased in any quantity. Fixed costs of ordering amount to about $$75$ for bookkeeping expenses, and holding costs are based on a $20$ percent annual rate. Bobbi estimates that the loss of customer goodwill for not being able to serve the syrup when re$-$quested amounts to $$25.$ Based on past experience, the weekly demand for the syrup is nor$-$mal with mean $12$ and variance $16($in bottles$).$ For the purposes of your calculations, you may assume that there are $52$ weeks in a year and that all excess demand is back ordered.a$.$How large an order should Bobbi be placing with her supplier for the maple syrup, and when should those orders be placed?b$.$What level of Type $1$ service is being provided by the policy you found in part $($a$)?$c$.$What level of Type $2$ service is being provided by the policy you found in part $($a$)?$d$.$What policy should Bobbi use if the stock$-$out cost is replaced with a Type $1$ service objective of $95$ percent?e$.$What policy should Bobbi use if the stock$-$out cost is replaced with a Type $2$ service objective of $95$ percent? $($You may assume an EOQ lot size.$)$f$.$Suppose that Bobbi$$s supplier requires a minimum order size of $500$ bottles. Find the reorder level that Bobbi should use if she wishes to satisfy $99$ percent of her customer demands for the syrup