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, $1500$ inpainting, and $1500$ in finishing. Brooklyn also has a contract that requires the company tosupply one of its customers with $500$ contemporary cabinets and $650$ farmhouse style cabinetseach week.Letx $=$ the number of contemporary style cabinets produced each weeky $=$ the number of farmhouse style cabinets produced each week$($a$)(4$ pts$)$ Develop the objective function, assuming that Brooklyn Cabinets wants to max$-$imize the total weekly profit.$($b$)(4$ pts$)$ Show the mathematical expression for each of the constraints on the three pro$-$cesses.$($c$)(4$ pts$)$ Show the mathematical expression for each of Brooklyn Cabinets contractualagreements.$($d$)(3$ pts$)$ Does the LP model necessarily contain non$-$negative constraints? Does the LPmodel necessarily contain linear constraints?