Given the weekly demand data below, simulate the operation of a fixed$-$order$-$quantity inventory system with a reorder point of $60,$ an order quantity of $100,$ and a beginning inventory of $100.$ The lead time is one week. All orders are placed at the end of the week and backordering is not allowed. What is the average end$-$of$-$week inventory on hand and the sales lost? $(15$ Points$)$

Week Beginning inventory Quantity on$-$order Demand Ending inventory Inventory position Order? $($yes$/$no$)$ Lost Sales

$153$

$240$

$336$

$438$

$555$

$634$

$730$

$831$

$940$

$1057$

$1130$

$1253$