What is the optimal number of each product to ensure optimal profit?

A company manufactures windows and doors in four types: wood windows, aluminum windows, balcony doors, and main doors.

 

Each of the products must pass through the following departments before they are shipped: Contracting, Painting, Assembly, and Testing.

 

The time requirements in each department (hours) for each unit produced and its corresponding profit values are summarized in this table:

 

 

 

Products

Constructing

Painting

Assembly

Testing

Profit/unit

Wood windows

0.5

3

2

5

90

Aluminium

1.5

1

4

1

120

windows

 

 

 

 

 

Balcony doors

1.5

2

1

0.5

150

Main doors

1.0

3

2

0.5

110

Department

255

500

480

315

 

Capacity(hours)

 

 

 

 

 

 

The market survey indicates that the minimum demand of four models is 30,30,40,50 units per hour respectively.

 

 

 

 

·        
What is the optimal number of each product to ensure optimal profit?

·        
What is the amount in dollars of the optimal profit in this scenario

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