EOQ calculation. The demand for toilet paper in a convenience store occurs at the rate of $100$ packets per month. Each packet contains a dozen rolls and costs $$8.$ Assume the order placement cost to be $$20$ per order and the holding cost rate to be $0\mathrm{.}25.$ Take one month to be the equivalent of four weeks.

a$)$ Determine the optimal order quantity, reorder interval, and optimal cost using the EOQ model.

b$)$ Suppose now that backordering of demand is allowed in the situation described in the previous question. The cost of backordering is $$\frac{10}{?}$ packet$/$year$.$ Use the EOQ model with backordering to determine the optimal order quantity, maximum backlog allowed, and optimal average annual cost.