One unit of A $($the end product$)$ is composed of two units of B and three units of C$.$ Each B is composed of one unit of F$.$ C is made of one unit of D$,$ one unit of E$,$ and two units of F$.$ Items B$,$ C$,$ and D have $50,60,$ and $25$ units of on$-$hand inventory, respectively. Items B and C use lot$-$for$-$lot $($LFL$)$ as their lot$-$sizing technique, while D$,$ E$,$ and F require multiples of $50,100,$ and $100,$ respectively, to be purchased. B has scheduled receipts of $30$ units in Period $1.$ No other scheduled receipts exist. Lead times are one period for Items B and D$,$ and two periods for Items C$,$ E$,$ and F$.$

The MPS for end$-$product A calls for the following start times and quantities $-$ Week $1(20$ units$),$ Week $5(60$ units$),$ Week $7(50$ units$).$