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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 ≥

Respuesta :

Answer:

See Step by step explanation

Step-by-step explanation:

Objective Function:  z

x =  number of contemporary style

y = number of farmhouse style

Costs

Carpentry costs:

15*2*x  +  15*2,5*y    =  30*x  +  37,5*y

Painting costs

12*1,5*x  +  12*1*y      =  18*x  +  12*y

Finishing costs

18*1,3*x  +  18*1,2*y    = 23,4*x  + 21,6*y

Total costs:

30*x  + 37,5*y + 18*x  + 12*y  + 23,4*x  + 21,6*y

71,4*x  +  71,1*y

z  =  90*x  +  85*y - ( 71,4*x  +  71,1*y )   to maximize

z  = 18,6*x  +  13,9*y  to maximize

Subject to:

First constraint:

Hours available in carpentry    3000

2*x  +  2,5*y ≤  3000

Second constraint

Hours available in painting  1500

1,5*x  +  1*y  ≤   1500

Third constraint

Hours available in finishing  1500

1,3*x  +  1,2*y  ≤ 1500

Fourth constraint

Minimum quantity of contemporary style  500

x ≥  500

Fifth constraint

Minimum quantity of farmhouse style   650

y  ≥  650

General constraints:

x  ≥  0     y  ≥  0   x , y  integers

Model:

z   =   90*x  +  85*y - ( 71,4*x  +  71,1*y )   to maximize

Subject to:

2*x  +  2,5*y ≤  3000

1,5*x  +  1*y  ≤   1500

1,3*x  +  1,2*y  ≤ 1500

x ≥  500

y  ≥  650

x  ≥  0     y  ≥  0   x , y  integers

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

Model z  =   90*x  +  85*y - ( 71,4*x  +  71,1*y )  

Subject to

2*x  +  2,5*y ≤  3000

1,5*x  +  1*y  ≤   1500

1,3*x  +  1,2*y  ≤ 1500

x ≥  500

y  ≥  650

x  ≥  0    y  ≥  0   x , y  integers.

We, wants to maximize the total weekly profit.

What is the meaning of constraints?

a constraint is a condition of an optimization problem that the solution must satisfy.

Objective function:  z

x =  number of contemporary style

y = number of farmhouse style

We have to find the cost

The carpentry costs is,

15*2*x  +  15*2,5*y    = 30*x  +  37,5*y

The painting costs is

12*1,5*x  +  12*1*y      =  18*x  +  12*y

The finishing costs is

18*1,3*x  +  18*1,2*y    = 23,4*x  + 21,6*y

Therefore the total costs is,

30*x  + 37,5*y + 18*x  + 12*y  + 23,4*x  + 21,6*y

71,4*x  +  71,1*y

z  =  90*x  +  85*y - ( 71,4*x  +  71,1*y )   to maximize

z  = 18,6*x  +  13,9*y  to maximize

Subject to the constraint;

The first constraint is,

The hours available in carpentry   3000

2*x  +  2,5*y ≤  3000

The second constraint is,

Hours available in painting  1500 so,

1,5*x  +  1*y  ≤   1500

The third constraint is,

Hours available in finishing  1500 so,

1,3*x  +  1,2*y  ≤ 1500

Fourth constraint is,

The minimum quantity of contemporary style  500 so,

x ≥  500

The fifth constraint is

The minimum quantity of farmhouse style   650 so,

y  ≥  650

The general constraints are,

x  ≥  0     y  ≥  0   x , y integers,

Therefore the Model z  =   90*x  +  85*y - ( 71,4*x  +  71,1*y )   to maximize,

Subject to

2*x  +  2,5*y ≤  3000

1,5*x  +  1*y  ≤   1500

1,3*x  +  1,2*y  ≤ 1500

x ≥  500

y  ≥  650

x  ≥  0    y  ≥  0   x , y  integers,

To learn more about the constraint visit:

https://brainly.com/question/6073946

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