Q$-3.(30$Marks$)$ A company is using dependent inventory modeling. Hence, the demand for product $C$ is $200$ units and shall be supplied in the eighth week. Each unit of $C$ requires $1$ unit of $K$ and $\frac{1}{2}$ unit of $U.$ Each unit of $K$ requires $1$ unit of $V,2$ units of W$,$ and $1$ unit of X$.$ Finally, each unit of $U$ requires $1$ unit of $Y$ and $3$ unit of $Z.$ All items are manufactured by the same firm. It takes two weeks to make $C,$ two weeks to make $K,$ three weeks to make $U,$ two weeks to make $V,$ three weeks to make $W,$ one week to make $x,$ two weeks to make $Y,$ and one week to make $Z.$

a$.$ Construct a material structure tree and formulate the gross material requirements plan for inventory data.

b$.$ When the first order of part $\text{'}Z\text{'}$ will be made?

c$.$ How many part $\text{'}W\text{'}$ will be ordered in total, and when?