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 x1, x2,.., xn which satisfy a system of linear equations (side conditions)
$$\begin{array}{*{20}{c}} {{a_{11}}{x_1} + {a_{12}}{x_2} + \ldots . + {a_{1n}}{x_n} = {b_1}} \\ {{a_{21}}{x_1} + {a_{22}}{x_2} + \ldots . + {a_{2n}}{x_n} = {b_2}} \\ {\begin{array}{*{20}{c}} { \ldots .} \\ {{a_{m1}}{x_1} + {a_{m2}}{x_2} + \ldots . + {a_{mn}}{x_n} = {b_m}} \end{array}} \end{array}$$
and a set of sign restrictions (non-negativity requirements)
$${x_1}0,{x_2}0, \ldots .,{x_n}0$$
and for which the linear function
$$f = {c_1}{x_1} + {c_2}{x_2} + \ldots . + {c_n}{x_n}$$
has a maximum.


Feasible Solution Basic Solution Linear Programming Problem Preference Function Fundamental Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag/Wien 1974

Authors and Affiliations

  • Sven Danø
    • 1
  1. 1.University of CopenhagenDenmark

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