Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary-style cabinets sell for $100and farmhouse-style cabinets sell for $110. 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 Process

Style Carpentry Painting Finishing

Contemporary 2.3 1.6 1.4

Farmhouse 2.7 1.2 1.4

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 is2,600in carpentry,1,300in painting, and1,300in finishing.

Brooklyn also has a contract that requires the company to supply one of its customers with475contemporary cabinets and750farmhouse-style cabinets each week.

Let

• 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.

carpentrypaintingfinishing

(c)

Show the mathematical expression for each of Brooklyn Cabinets' contractual agreements.

contemporaryfarmhouse