Based on the historical data, the weekly demand for the americano is normal with mean $12$ and variance $16($in bottles$)($Assume $52$ weeks in a year and all excess demand is backordered$)$ Question $1)(25$ points $=19+6$ The cafeteria on campus started to sell high quality instant coffee americano. These instant coffees come in individual packs and cost $4$TL$/$serving and the lead$-$time for replenishment is $4$ weeks. Fixed cost of ordering is about $75$TL and holding cost is $2$TL$/$item annually The loss of customer goodwill is estimated to be $25$TL per packet $($can be used as penalty for unsatisfied demand$).$ SHOW YOUR WORK! a$)(7+6+6=19$ points$)$ How large an order should cafeteria be placing for americano to minimize total cost subject to $90\%$ type $2$ service level? $($at least $2$ iterations$)$ b$.$ What should be the reorder level $($quantity$)$ and expected cycle time? What is the expected time from the receipt of an order until the placement of next order? C$.$ b$)(6$ points$)$ What level of Type $1$ service is being provided by the policy you found in part $($a$)?$