In this note we consider the validity of substituting a linear goal for a fractional goal in a mathematical program and provide a simple geometric interpretation that contrasts the essential differences between the two programs.

For an ordinary linear program it is well known that, if the resources are evaluated at marginal prices determined by an optimal dual solution, then this imputed value is identical with the value of the primal objective function. For a convex program with a nonlinear objective function and...

The ordinary finite, two-person, zero-sum game is completely defined by specifying an m \times n game matrix A. The optimal strategies for both players, and the value of the game, can be obtained by solving a dual pair of linear programming problems. In this paper a semi-infinite game is defined;...