Ellen Farr is responsible for purchasing forgings and castings for Farr Machining Corporation$$s raw material stockroom. Ellen$$s job is to purchase enough castings and forgings to meet weekly demand for these items by the firm$$s fabrication shop in producing machined parts. Forecast weekly requirements for one item $($the input shaft forging$)$ and cost information for this item are as follows:

Week

$12345678910$

Forecast $44521004204602003001004050$

Ordering cost $=$ $$250.$

Inventory carrying cost $=$ $$5/$unit$/$week$.$

Calculate the orders Ellen would place and the total cost incurred using:

$($a$)$ Economic Order Quantity $($EOQ$)$

$($b$)$ Periodic Order Quantity $($POQ$)$

$($c$)$ Part Period Balancing $($PPB$)$