File:Mmult factory.pdf

Summary

Description
English: Example application of matrix multiplication in economics, from Peter Stingl (1996) (in german) Mathematik für Fachhochschulen – Technik und Informatik (5th ed.), Munich: Carl Hanser Verlag ISBN: 3-446-18668-9. Exm.5.4.10, p.205-206.

The highlighted paths in production flow (upper part) correspond to the highlighted computation of the lower left field in the product matrix (lower part).

See en:Matrix_multiplication#Resource_allocation_in_economics for full description of the scenario.
Date
Source Own work
Author Jochen Burghardt
Other versions File:Mmult factory.pdf * File:Mmult factory svg.svg
LaTeX source code
\documentclass[12pt]{article}
\usepackage[pdftex]{color}
\usepackage[paperwidth=135mm,paperheight=100mm]{geometry}
\setlength{\topmargin}{-36mm}
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% lowlight backgrounds
\definecolor{bBas}      {rgb}{0.99,0.95,0.95}% basic good
\definecolor{bFin}      {rgb}{0.95,0.99,0.95}% final product
% lowlight foregrounds
\definecolor{fBas}      {rgb}{0.99,0.70,0.70}% basic good
\definecolor{fFin}      {rgb}{0.70,0.99,0.70}% final product
% lowlight connections
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\definecolor{bMul}      {rgb}{0.99,0.99,0.99}% multiplicity
\definecolor{fMul}      {rgb}{0.80,0.80,0.99}% multiplicity
% lowlight zero connections
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% highlight backgrounds
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\definecolor{bINT}      {rgb}{0.99,0.99,0.70}% intermediate product
\definecolor{bFIN}      {rgb}{0.70,0.99,0.70}% final product
% highlight foregrounds
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\definecolor{fINT}      {rgb}{0.70,0.70,0.00}% intermediate product
\definecolor{fFIN}      {rgb}{0.00,0.70,0.00}% final product
% highlight connections
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\definecolor{fMUL}      {rgb}{0.00,0.00,0.99}% multiplicity

\begin{document}

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$$
\left(
\begin{array}{ccc}
\0 1 & \0 0 & \0 1 \\
\0 2 & \0 1 & \0 1 \\
\0 0 & \0 1 & \0 1 \\
\9 1 & \9 1 & \9 2 \\
\end{array}
\right)
        \cdot
\left(
\begin{array}{ccc}
\9 1 & \0 2 & \0 1 \\
\9 2 & \0 3 & \0 1 \\
\9 4 & \0 2 & \0 2 \\
\end{array}
\right)
        =
\left(
\begin{array}{ccc}
\0  5 & \0 4 & \0 3 \\
\0  8 & \0 9 & \0 5 \\
\0  6 & \0 5 & \0 3 \\
\9 11 & \0 9 & \0 6 \\
\end{array}
\right)
$$
\end{document}

Licensing

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w:en:Creative Commons
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Category:CC-BY-SA-4.0#Mmult%20factory.pdf
Category:Self-published work Category:Matrix multiplication Category:Images with LaTeX source code Category:Files by User:Jochen Burghardt Category:Resource planning
Category:CC-BY-SA-4.0 Category:Files by User:Jochen Burghardt Category:Images with LaTeX source code Category:Matrix multiplication Category:Resource planning Category:Self-published work