Linear Programming This section introduces the general method called the simplex algorithm, which is designed to solve any linear program. The information that can be secured from the simplex method goes beyond determining the optimum values of the variables. Indeed, it provides important economic interpretations of the problem and shows how sensitivity analyses can be carried out algebraically.
The simplex method solves linear programming in iterations where the same computational steps are repeated a number of times before the optimum are reached.
The Standard Form of the LP Model:
An LP model may include constraints of the types ≤, =, and ≥. Moreover, the variables may be non-negative or unrestricted in sign. In order to develop a general solution method, the LP problem must be put in a common format, which we call the standard form. The properties of the standard LP form are:
1) All constraints are the equations with non-negative right-hand side.2) All the variables are non-negative.3) The objective function might be maximization or minimization.