Brooklyn Cabinets is a manufacturer of kitchen cabinets The

Brooklyn Cabinets is a manufacturer of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemporary and farmhouse. Contemporary style cabinets sell for $90 and farmhouse style cabinets sell for $85. Each cabinet produced must go through carpentry, painting, and fiishing 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 2.0 1.5 1.3
Farmhouse 2.5 1.0 1.2

Carpentry costs $15 per hour, painting costs $12 per hour, and fiishing costs $18 per hour, and the weekly number of hours available in the processes is 3000 in carpentry, 1500 in painting, and 1500 in fiishing. 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.

Let

x = the number of contemporary style cabinets produced each week

y = the number of farmhouse style cabinets produced each week

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

The objective function is maximize

Show the mathematical expression for each of the constraints on the three processes.

Hours available in carpentry: x1 + y1

Hours available in painting: x2 + y2

Hours available in fiishing: x3 + y3

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

x

y

Solution

Total cost of process in :

For contemporary style = 2 x $15 + 1.5 x $12 + 1.3 x $18 = $71.4

For farmhouse style = 2.5 x $15 + 1 x $12 + 1.2 x $18 = $71.1

Profit for contemporary style= $90-$71.4 =$18.6

Profit for farmhouse style = $85-$71.1= $13.9

Here the objective function is to maximize profit.

Let us assume we sell x contemporary and y farmhouse style:

Then the profit function is:

P = $18.6x + $13.9y     this is objective function

The constraints are:

2x + 2.5y <= 3000

1.5x + y <= 1500

1.3x + 1.2y <= 1500

Brooklyn Cabinets\' contractual agreement

x >=500

y>= 650