$2.$ Product A is an end item and is made from three units of B$,$ four units of C and two units of D$.$ B is made of three units of E and two of F$.$ C is made of two units of F and one of D$.$ A and B have a lead time of one week. C and D have lead times of two weeks, and E and F have lead times of three weeks. Lot sizes for A$,$ B and D are L$4$L$.$ Item C has a lot size of $60.$ E and F have a lot size of $100.$ There is $40$ units of item B on hand, and $20$ units of item A$.$ There is a scheduled receipt for $50$ units of item F in week three.

A$)$ Show the bill of materials $($product structure tree$)$

B$)$ If $120$ units of A are required in Week $8,$ develop the MRP planning schedule, specifying when items are to be ordered and received.