A product line has two models: X and Y$.$ Model X consists of $4$ components: a$,$ b$,$ c$,$

and d$.$ The number of processing operations required to produce these four components

are $2,3,4,$ and $5,$ respectively. Model Y consists of $3$ components: e$,$ f$,$ and g$.$ The

number of processing operations required to produce these three components are $6,7,$

and $8$ respectively. The annual quantity of Model X is $1000$ units and of Model Y is

$1500$ units.