THE CENTRAL MATHEMATICAL PROBLEM
RAND CORP SANTA MONICA CA
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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.
- Operations Research