$1.$ Consider the following information about an end$-$product item:

Ordering cost $=$ $$45/$order$.$

Average usage $=12$ units$/$week$.$

Inventory carrying cost $=$ $$1/$unit$/$week$.$

a$.$ How many orders should we place per year $(52$ weeks$)$ to replenish inventory of the item

based on average weekly demand?

b$.$ Given the following time$-$phased net requirements from an MRP record for this item, determine the sequence of planned orders using economic order quantity and periodic order

quantity procedures. Assume lead time equals zero and current on$-$hand inventory equals zero.

Calculate the inventory carrying cost on the basis of weekly ending inventory values. Which

procedure produces the lowest total cost for the eight$-$week period?