A retailer would like to determine the optimum order quantity based on the annual demand of the product, holding cost, and setup cost $($ordering cost$).$ The annual demand for the product is $2000$ units. The holding cost of the product per year is $$1$ per item. The setup cost per order is $$50$ per order. The retailer operates $250$ days in a year.

$($a$)$ Based on the data given above, find the optimum order quantity $($number of items per order$).$

$($b$)$ If the company orders the optimum order quantity for each order, then how many orders will the company make during the year?

$($c$)$ What would be the time between two orders?

$($d$)$ What is the total holding and ordering cost?

$($e$)$ Calculate the Reorder point, if the lead time for each order is $7$ days