devoted to each style of cabinet.

$\backslash$table$[[,$Hours per Process$],[$Style$,$Carpentry,Painting,Finishing$],[$Contemporary$,2\mathrm{.}4,1\mathrm{.}7,1\mathrm{.}5],[$Farmhouse$,2\mathrm{.}8,1\mathrm{.}0,1\mathrm{.}2]]$

$1,200$ in finishing.

Brooklyn also has a contract that requires the company to supply one of its customers with $450$ contemporary cabinets and $625$ farmhouse$-$style cabinets each week.

Define $x$ and $y$ as follows.

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

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

$($a$)$ Develop the objective function, assuming that Brooklyn Cabinets wants to maximize the total weekly profit.

Max

$($b$)$ Show the mathematical expression for each of the constraints on the three processes.

carpentry

painting

finishing

$($c$)$ Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements.

contemporary

farmhouse