$3.$ 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? $(4$ points$)$

$328\mathrm{.}63$ bags this is the answer show me the work

b$)$ What is the reorder point in view of the lead time? $(2$ point$)$

$75$ bags. this is the answer show me the work

c$)$ What are the total costs under EOQ? $(3$ points$)$

$$4582\mathrm{.}16/$yr answer. show me the work

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? $(5$ points$)$

Q$*=89\mathrm{.}66$ bags

SS $=14\mathrm{.}67$ bags

e$)$ What are the total inventory costs? $(3$ points$)$

$$85\mathrm{.}83/$yr this is the answer show me the work