and finishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet.

$\backslash$table$[[$Style$,$Carpentry,$\backslash$table$[[$Hours per$],[$Process Painting$]],$Finishing$],[$Contemporary$,2\mathrm{.}0,1\mathrm{.}5,1\mathrm{.}3],[$Farmhouse$,2\mathrm{.}5,1\mathrm{.}0,1\mathrm{.}2]]$

Carpentry costs $$15$ per hour, painting costs $$12$ per hour, and finishing costs $$18$ per hour; and the weekly number of hours available in the processes is $3000$ in carpentry, $1500$ in painting, and $1500$ in finishing. Brooklyn also has a contract that requires the company to supply one of its customers with $500$ contemporary cabinets and $650$ farmhouse style cabinets each week.

Define $x$ and $y$ as follows. LO $4$

$x=$ the number of contemporary style cabinets produced each week

$y=$ the number of farmhouse style cabinets produced each week