The demand for subassembly S is $150$ units in week $7.$ Each unit of S requires $1$ unitnothing of T and $2$ units of U$.$ Each unit of T requires $2$ units of$$ V$,2$ units of$$ W$,$ and $1$ unitnothing of X$.$ Finally, each unit of U requires $1$ unitnothing of Y and $3$ units of Z$.$ One firm manufactures all items. It takes $2$ weeks to make$$ S$,1$ weeknothing to make$$ T$,2$ weeks to make$$ U$,2$ weeks to make$$ V$,3$ weeks to make$$ W$,1$ weeknothing to make$$ X$,2$ weeks to make$$ Y$,$ and $1$ weeknothing to make Z$.$