$15\mathrm{.}2$ A company assembles three distinct finished SKUs, items F$1,$ F$2,$ and F$3.$ The bills of materials for these items, their components, and quantities, are as follows:

Item FL: Composed of $1$ unit of A$1,$ A$2,$ and A$3$ and $2$ units of A$4$

Item F$2$: Composed of $1$ unit of A$1,$ A$2,$ and A$4$

Item F$3$: Composed of $1$ unit of Al and A$4$

Item A$1$: Composed of $1$ unit of A$2$ and BI

Item A$2$: Composed of $1$ unit of A$4,$ B$1,$ and B$2$

Item A$3$: Composed of $1$ unit of $\backslash ($ B $1\backslash )$ and $\backslash ($ B $2\backslash )$ and $3$ units of B$3$

Item A$4$: Composed of $2$ units of B$3$

Item BL: Composed of $1$ unit of B$3$ and Cl

Item B$2$: Composed of $1$ unit of C$1$ and C$2$

Item B$3$: Composed of $1$ unit of C$1,$ C$2,$ and C$3$

Items C$1,$ C$2,$ and C$3$ are purchased parts. In addition, items Al and A $2$ are sold directly to customers as spare parts.

Develop a level$-$by$-$level coding for the thirteen items.

$15\mathrm{.}3$ Suppose that the offects for the operations involved in Problem $15\mathrm{.}2$ are as follows:

Considering only F$1$ and its components,

a$.$ What minimum horizon should be used for the master production schedule?

b$.$ If the only customer order is for $10$ units of item F$1$ in week $15$ and there is no initial on$-$hand or on$-$order stock for any items, establish the procure ment and production schedule for item F$1$ and all its components.