The demand for subassembly S is $110$ units in week $7.$ Each unit of S requires $1$ unit of T and $1$ unit of U$.$ Each unit of T requires $2$ unit of$$ V$,2$ unit of$$ W$,$ and $2$ unit of X$.$ Finally, each unit of U requires $2$ unit of Y and $3$ units of Z$.$ One firm manufactures all items. It takes $2$ weeks to make$$ S$,1$ week to make$$ T$,2$ weeks to make$$ U$,1$ week to make$$ V$,2$ weeks to make$$ W$,1$ week to make$$ X$,2$ weeks to make$$ Y$,$ and $2$ week to make Z$.$