Interpretation of the Lagrange Multipliers
By Dr
Muhammad Al-Salamah
A company produces wooden chairs for local consumption in the Eastern Province. The company is capable of producing three types of chairs. The selling prices in thousands of the chairs are Type Prices
|
Type |
Prices |
|
1 |
1 |
|
2 |
3 |
|
3 |
1 |
The raw material (wood) comes in pieces and the consumption of the wood pieces for each type is Type Pieces of wood
|
Type |
Pieces of wood |
|
1 |
1 |
|
2 |
4 |
|
3 |
3 |
The company has a supply of 12 wood pieces to manufacture chairs of all types. The production mix of chairs will be determined on the basis of the largest revenue. Introducing the variable xi = number of chairs produced of type i, the revenue can be written as
in thousand riyals. The production is related to the supply by the mathematical relation
Answer the following questions:
- What will be the optimal production mix of chairs that will bring the maximum revenue to the company if the company has 12 wood pieces?
- What is the ‘fair’ price for the wood pieces?
- By how much the optimal objective function value is going to increase or decrease if the wood pieces are increased by one piece?