THE CENTRAL MATHEMATICAL PROBLEM

Abstract

Symbols are introduced to distinguish various activities, items, the assumed constant flows and costs (or profits) per unit level of activity, the activity levels and the quantities of demand or availability of various items. The central problem is then stated in standard algebraic form. It is shown that the problem of minimizing a linear form where the unknowns satisfy a system of equations in non-negative variables is equivalent to one where the variables satisfy a system of linear inequalities. It is stated without proof that an optimizing solution belongs to a class of feasible solutions that 'involve' no more variables than equations. The simplex method is illustrated by showing for this class a way of testing the optimality of a solution and constructing a sequence of improved feasible solutions.

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Document Details

Document Type
Technical Report
Publication Date
Jul 09, 1956
Accession Number
AD0605057

Entities

People

  • G. B. Dantzig

Organizations

  • RAND Corporation

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Blast Furnaces
  • Cartesian Coordinates
  • Chemical Equilibrium
  • Coefficients
  • Commodities
  • Computer Programming
  • Equations
  • Hard Copy
  • Inequalities
  • Linear Programming
  • Mathematical Models
  • Models
  • Simplex Method
  • Standards

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Industrial Economics
  • Operations Research