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I'm learning linear programming's basic concepts. In following inequality:

$$ \begin{align} \text{Minimize }c_1x_1 + c_2x_2 + \cdots+ c_nx_n \\ \\ \text{Subject to }a_{11}x_1 + a_{12}x_2 +\cdots+a_{1n}x_n & \geqslant b_1 \\ \\ a_{21}x_1 + a_{22}x_2 +\cdots+a_{2n}x_n & \geqslant b_2 \\ & {}\ \vdots\\ a_{m1}x_1 + a_{m2}x_2 +\cdots+a_{mn}x_n & \geqslant b_m \\ \\ x_1,x_2,\ldots,x_n & \geqslant 0 \end{align} $$

My question is : Why we call $a_{ij}$ "technological coefficients" ? What is technology ? And why is it technological ? I don't know the meaning of "technological" in here.

Thanks in advance

Update: Book: Linear Programming and Network Flows. Written by: Mokhtar S. Bazaraa. 3rd Edition. Page 2

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It would be immensely helpful if you mention the book/paper/whatever you got this term from... – J. M. Oct 15 '11 at 5:38
@J.M. Linear Programming and Network Flows. Written by: Mokhtar S. Bazara. 3rd Edition. Page 2 – linker Oct 15 '11 at 5:41
Your TeX formatting technique was abominable. I've cleaned it up. – Michael Hardy Oct 15 '11 at 15:47
@MichaelHardy : thanks – linker Oct 15 '11 at 17:22
@linker: I think it's just that the constraints in a particular scenario being modeled with an LP often represent some technological restriction on what's possible in that scenario. Thus it makes sense, I guess, to call the coefficients of the constraints "technological coefficients." I really don't think there's any deeper reason than that. – Mike Spivey Oct 16 '11 at 17:54

2 Answers 2

The term is strange but it is not a mathematical term. My guess is that the term originates from the Economics field where it is comonly used in theories like input-output (e.g Link-1). Looking back at the history of Linear Programming and its early economical motivations, it is possible that early papers used the terminology of the problem filed (namely, Economics) to present the theory, and it has been used every since.

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They also called input-output coefficients, and they represents the amount of resource $ i$ consumed per unit of variable $x_j$.

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