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LINEÆR PROGRAMMERING

SVEN DANØ
Nordisk Matematisk Tidskrift
Vol. 4, No. 3 (1956), pp. 121-138
Published by: Mathematica Scandinavica
Stable URL: http://www.jstor.org/stable/24524427
Page Count: 18
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LINEÆR PROGRAMMERING
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Abstract

The general problem of "linear programming" can be formulated as follows: Find a set of non-negative numbers x1, x2,..., xn, which satisfy a system of linear equations (1) ai1x1+ai2x2+...+ainxn = bi (i = 1, 2,..., m), and for which the linear function f = c1x1+c2x2+...+cnxn has a maximum (or minimum). The case of inequalities in (1) can be reduced to the above form, by introducing the non-negative differences between the sides of the inequalities as new "slack variables". After a geometrical treatment of the simple case m=1, n=2, the following theorem is proved: If the general problem (with m

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