Elements of the Mathematical Theory of Linear Programming

  • Sven Danø


The general problem of linear programming can be formulated as follows : Find a set of numbers x 1, x2, ..., xn which satisfy a system of linear equations (side conditions)
$$ \eqalign{ & {a_{11}}{x_1} + {a_{12}}{x_2} + ....{a_{1n}}{x_n} = {b_1} \cr & {a_{21}}{x_1} + {a_{22}}{x_2} + ....{a_{2n}}{x_n} = {b_2} \cr & .... \cr & {a_{m1}}{x_1} + {a_{m2}}{x_2} + .... + {a_{mn}}{x_n} = {b_m} \cr} $$
and a set of sign restrictions (non-negativity requirements)
$$ {x_1} \geqslant 0,\;{x_2} \geqslant 0,....,{x_n} \geqslant 0$$
and for which the linear function
$$ {\text{f = }}{{\text{c}}_1}{x_1} + {c_2}{x_2} + \ldots + {c_n}{x_n}$$
has a maximum.


Feasible Solution Basic Solution Preference Function Fundamental Theorem Slack Variable 
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Copyright information

© Springer-Verlag Wien 1963

Authors and Affiliations

  • Sven Danø
    • 1
  1. 1.University of CopenhagenDänemark

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