Linear Programming

A = Wooden Windows

B = Aluminum Windows

C = Balcony Doors

D = Main Doors

Objective Function

There is an objective function and that function is based on profit maximization

Maximize:

90 A + 120 B + 150 C + 110 D

Each unit of wooden windows contributes 90 dollars to the total profit, Aluminum windows contribute 120 to the total profit, Balcony doors contribution margin is 150 and the contribution margin of main doors is 110

There are two constraints that should be taken into account. The first is capacity constraints, while the second is demand constraints.

Capacity Constraint

Each of the departments have their own capacities and in these capacities they must operate.

Construction

0. 5 A + 1. 5 B + 1. 5 C + 1 D <= 255

This indicates that Wooden window takes up 0.5 hours of construction, Aluminum windows consume 1.5 hours of construction, Balcony doors have a consumption of 1.5 hours and the main door is made in 1 hour. The total hours that construction department has is 255 hours.

Painting

3 A + 1 B + 2 C + 3 D <= 500

This indicates that Wooden window takes up 3 hours of painting, Aluminum windows consume 1 hour of painting, Balcony doors have a consumption of 2 hours and the main door is made in 3 hours. The total hours that painting department has is 500 hours.

Assembly

2 A + 4 B + 1 C + 2 D <= 480

This indicates that Wooden window takes up 2 hours of assembly, Aluminum windows consume 4 hours of assembly, Balcony doors have a consumption of 1 hour and the main door is made in 2 hours. The total hours that assembly department has is 480 hours.

Testing

5 A + 1 B + 0. 5 C + 0. 5 D <= 315

This indicates that Wooden window takes up 5 hours of testing, Aluminum windows consume 1 hour of testing, Balcony doors have a consumption of 2 hours and the main door is made in 3 hours. The total hours that testing department has is 315 hours.

Demand Constraints

Wooden Windows

A > = 30

This constraint determines that the since the demand of wooden windows is 30, so the supply should be more than or equal to 30.

Aluminum Windows

B > = 30

This constraint determines that the since the demand of Aluminum windows is 30, so the supply should be more than or equal to 30.

Balcony Doors

C > = 40

This constraint determines that the since the demand of balcony doors is 40, so the supply should be more than or equal to 40.

Main Doors

D > = 50

This constraint determines that the since the demand of main doors is 50, so the supply should be more than or equal to 50.

Results

There are two tables that are given below, the first one is based on the inputs, while the second one the outputs, incorporating the decision variables.

Inputs

Outputs

Conclusion on Linear Programming

Profit Maximization is only possible when the wooden windows are 32, Aluminum windows are 30, Balcony Doors are 83, and Main doors are 67. A combination of this would increase the capacity of the variables to $26,300 of total profit.

  Appendix