An article by George Dantzig, the ‘father of linear programming’. The problem of minimizing or maximizing a function of several variables subject to constraints when all the functions are linear is called a ‘linear program’. Linear programs can be used to approximate the broad class of convex functions commonly encountered in economic planning. Thousands of linear programs are efficiently solved with the simplex method, an algorithm. Solving a model with alternative activities requires software not only for solving on computers large systems of equations but also for selecting the best combination from an astronomical number of possible combinations of activities.
KeywordsBimatrix games Convex program Dantzig, G. Decomposition principle Dantzig, G. B. Kantorovich, L. V. Koopmans, T. C. KuhnTucker conditions Lagrange multipliers Leontief input–output model Linear programming Mathematical programs Mini-max theorem Mixed strategies Simplex method for solving linear programs von Neumann, J.
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