You want to plan for an item whose gross requirements are given in the following table. The lot sizing method is FOQ $(20),$ the leadtime is $1$ week, the available on$-$hand inventory is $40$ units, and the safety stock requirement is $10$ units. There is a scheduled receipt of $20$ units in Week $1.$

Week $1$ Week $2$ Week $3$ Week $4$

Gross Requirements $402050$

Scheduled receipts $20$

Projected Available Balance

Planned Receipts

Planned Order Releases

$($a$)$ What is the projected available balance at the end of Week $1?$

units

$($b$)$ What should be the planned receipt in Week$2?$

units

$($c$)$ What should be the planned order release in Week $3?$

units