Using the product tree shown, determine the following: $($A$)$ the quantity of component that will be needed to assemble $100$ units of P$,$ assuming no on$-$hand inventory of any components exists. $($B$)$ the quantity of component K needed to assemble $100$ units of P$,$ given on$-$hand inventory of $50$ A$\text{'}$s$,50$ B$\text{'}$s and $30$ C$\text{'}$s$.$ A$(2$ B$(5$ C$3$ K$(2(3$ C$(2$ D K$(3$ Answer: $($assuming no A$.$ Qty of K needed to assemble $100$ units of P inventory$)($assuming B$.$ Qty of K needed to assemble $100$ units of P inventory above.$)$

An explanation of how to work this out would be greatly appreciated :$)$