Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary-style cabinets sell for $110 and farmhouse-style cabinets sell for $100. Each cabinet produced must go through carpentry, painting, and finishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet.

Hours per ProcessStyleCarpentryPaintingFinishingContemporary2.31.61.4Farmhouse2.71.11.3

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 2,600 in carpentry, 1,300 in painting, and 1,300 in finishing.

Brooklyn also has a contract that requires the company to supply one of its customers with 525 contemporary cabinets and 750 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