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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