Develop a material requirements plan for item $P$ and its components, given the tree below. Assume that all lead times are one week, and that lot$-$for$-$lot ordering is used except for item F$,$ which is ordered in multiples of $400$ units.

One hundred units of $P$ are needed at the start of each of weeks $4$ and $8.$

Beginning inventories are: $20P,100A,$ and $200F.$ Scheduled receipts are: $800F$ at the start of week $1.$