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Develop a material requirements plan for end item P and its components, given the following tree. 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 $100$ units.

$50$ units of P should be available at the start of week $5$ and at the start of week $8.$ Beginning inventories are: $20$ Ps$,30$ As$,$ and $100$ Fs$.$

Scheduled receipts are: $100$ Fs at the start of week $1.$