Matrices: matrix multiplication: economics example
Solving econimics problems often involves matrix calculations.
Let's assume you have the task of determining the amount of raw material necessary to produce
two different products. The final products in turn consist of intermediate products.
The problem is interlinked with the amount of raw material, intermediate product and final
product. To solve the problem, we need to perform multiple matrix multiplication.
Let's assume the following for our two final products:
- Amount of final product 1: 11
- Amount of final product 2: 5
To produce these two final products, the following amounts of intermediate products are necessary:
- For the final product 1:
- 3 units of intermediate product 1
- 4 units of intermediate product 2
- For the final product 2:
- 7 units of intermediate product 1
- 3 units of intermediate product 2
Again, to produce the intermediate product, the following amount of raw material is necessary:
- For the intermediate product 1:
- 1.5 units of raw material 1
- 4 units of raw material 2
- For the intermediate product 2:
- 1 units of raw material 1
- 3 units of raw material 2
- 2.5 units of raw material 3
In matrix formulation, we have to solve the following problem:
The course of action with MasterAllRound is:
- Go to "Matrix multiplication (ABC)"
- Enter the size of the matrices
- Fill out the cells of the single matrices
- Start the calculation by clicking on "Multiply (ABC)"
- You obtain the result matrix:
are necessary to produce 11 units of the final product 1 and 5 units of the final product 2.
- 161 units of raw material 1,
- 449 units of raw material 2 and
- 147.5 units of raw material 3
(To MAR Plus)