$3.$ Your dorm has decided to go in together on a communal shelter for dogs. Dog food can be kept for a long time when stored properly. Because you stop by the shelter every day to check on the dogs, you have a continuous review system. Dogs eat $15$ bags of dog food every day at a constant rate. Every time you place an order for bulk dog food from the manufacturer, it takes $5$ days for delivery and costs $3$ dollars $($independent of the number of bags$).$ Thanks to ordering in bulk, each bag of dog food only costs $1$ dollar. The annual cost of storing dog food is $0\mathrm{.}25$ dollars per bag per year. Assume $300$ days per year. a$)$ What is the economic order quantity? $328\mathrm{.}63$ bags b$)$ What is the reorder point in view of the lead time? $75$ bags c$)$ What are the total costs under EOQ? $$4582\mathrm{.}16/$yr For the remaining questions, dogs start to eat more or less depending on how much they play outside. Demand now becomes variable. After a few months, you find that the demand is normally distributed with an average demand of $15$ bags per day, and a standard deviation of $4.$ d$)$ With this variable demand, assuming a service level of $95\%,$ what is the reorder point? What is the safety stock? Q$*=89\mathrm{.}66$ bags SS $=14\mathrm{.}67$ bags e$)$ What are the total inventory costs? $$85\mathrm{.}83/$yr