A fast-food restaurant receives supplies from its distributor every other day just prior to opening for business. The manager places an order for new supplies just prior to opening for business on the...

A fast-food restaurant receives supplies from its distributor every other day just prior to opening for business. The manager places an order for new supplies just prior to opening for business on the days between receiving orders. To clarify the situation, we number the days sequentially, 1, 2, 3,…, and specify that orders can only be placed on odd-numbered days and orders are received at the beginning of the following (even-numbered) day. The manager decides how much of each item to order by checking the inventory on hand just prior to ordering. One item that he orders is frozen hamburger patties. If he finds 600 or fewer patties in inventory on the day of an order, then he orders 1000 patties minus the number of patties in inventory. If there are more than 600 patties on hand, then he does not order any more. Notice that if he chooses not to order, then it will be at least 3 days before receiving another shipment, since his next order cannot be placed for 2 more days. Listed below is the number of hamburgers on hand at the beginning of each day for a 14-day study period. The inventory on hand on a day that an order is received includes the order

Because it is expensive to keep supplies on hand, the manager would like to reduce the reorder point from 600 patties to 500 patties. Can he do this without running out of hamburger patties? Perform sample-path decomposition; then generate the sample path that would result from the new reorder point. If he runs out, record how many hamburger sales that he loses. (Hint: The system input is the number of hamburgers demanded each day.)