Brooklyn Cabinets is a Manu facture of kitchen cabinets The

Brooklyn Cabinets is a Manu facture of kitchen cabinets. The two cabinetry styles manufactured by Brooklyn are contemplator and farmhouse. Contemporary style cabinets sell for $90 and farmhouse style cabinets sell for $85. Each produced must go throng carpentry, painting, and finishing processes. The following table summarizes how much time in each process must be devoted to each style of cabinet.

Solution

Answer:

The revenue for the two types are:

For contemporary style = $90

For farmhouse style = $85

Cost of carpentry = $15 per hour

Cost of painting = $12 per hour

Cost of finishing = $18 per hour

Now,

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

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