Given the following product tree: $(10$ Points$)$

If $17P\text{'}$s are needed in week $7$ and no on$-$hand inventory exists, how many M$\text{'}$s are required? $(3$ points If we have $20$ in A inventory and $10$ in $M$ inventory how many M$\text{'}$s are now required? $(3$ points$).$ If each component has a $1$ week lead time, when must production start on each component? $(4$ points$).$