ABSTRACT
This chapter explains some of geometric properties to linear programs with multiple variables. It reviews a number of geometric properties of the multidimensional feasible region. Since the figures cannot be visualized in more than three dimensions, it utilizes inductive reasoning to interpret those geometric properties. The chapter introduces one of those properties, the Karush-Kuhn-Tucker (KKT) conditions, which require that, in the optimal vertex, the normal vector or gradient z of the objective function must lay between the gradients vi of the active constraints. A linear program in two dimensions has a number of geometric properties that determine its optimal solution. For example, at the optimum point, at least one constraint is active, and such optimum may not be unique if the objective function has the same slope as the active constraint. The KKT conditions are necessary and sufficient conditions for a solution to be optimal in a linear program.
