A local supermarket needs your help in determining the optimal ordering policy for a stainless$-$steel vacuum bottle. The demand for this water bottle is $20$ units per day. The store pays a unit cost of $$15$ per bottle and a fixed ordering cost of $$150$ per order. The annual unit holding cost of inventory is estimated to be $25\%$ of the unit cost. The store operates $250$ days a year.

a$.$ Determine the Economic Order Quantity $($EOQ$).$ Compute the time between two orders and the total annual relevant inventory cost $($i$.$e$.,$ sum of holding and ordering costs$)$ for stainless$-$steel vacuum bottle in the EOQ model.

b$.$ Compute the reorder point assuming that the order lead time is $4$ workdays.

c$.$ Suppose that supplier requires orders to be placed in multiples of $100$ units. What order quantity would you now suggest to the store to meet the supplier's mandate while minimizing total annual costs? What is the increase in the total annual relevant inventory cost due to this requirement compared to your answer in part $($a$)?$