$[20$ points$]$ firm makes a product $($product A$)$ from five components $($intermediate Items B$,$ D$,$ and E$,$

and purchased item C$).$ The bill of materials $($BOM$)$ of product A shows the required number of subcomponents to make a parent component is given in the parentheses. For example, to make $1$ unit of

A$,1$ unit of B and $2$ units of D are required. To make $1$ unit of B$,2$ units of C are required, and so on$.$

The gross requirement for product A is $200$ units in week $8.$ Inventory on$-$hand for the items are given

in the table below. Calculate the net requirement for the six components.

Item On$-$Hand Inventory

A $50$

B $60$

C $90$

D $70$

E $25$

F $10$