$3.$ Your dorm has decided to go in together on a communal shelter for dogs.Dogfood 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$)$ Whatistheeconomicorderquantity?$(4$points$)$