Problem $7$: $(10$ points$)$

Each unit of a finished product $Z$ requires one unit of $x,$ two units of $Y,$ and three units if $T.$ Each unit of $x$ requires two units of $U$ and one unit of $T.$ Each unit of $Y$ requires one unit of $V$ and two units of $U.$ Each unit of $T$ requires three units of $U$ and one unit of $V.$ The demand for the finished product $Z$ is $100$ units in week $7.$ It takes two weeks to manufacture $Z,$ one week to make $x,$ two weeks to make $Y,$ two weeks to make $T,$ one week to purchase $U,$ and also one week to purchase $V.$

a$-$ Construct the BOM of $Z$

b$-$ What the minimum cumulative planning horizon

c$-$ Construct a net requirements plan from the BOM and the following inventory data

$\backslash$table$[[$Item$,T,x,Y,T,U,V$