In this module, we will introduce a commercial LP software package, LINGO. A very small problem (Wyndor Glass Co. prototype example) was introduced in Module 1 to illustrate the LP model, a problem small enough to solve graphically. We will now generalize the LP model for any application or problem size.

George Dantzig’s development of the simplex method made it possible to systematically solve incredibly complex problems. ​Simplex method, combined with powerful computer applications that perform the calculations contained in the simplex method, have made the use of Linear Programming applicable in many different fields. The correct use of the simplex method gives you the ability to construct and answer complex questions consisting of hundreds or thousands of dimensions, and makes you an invaluable member of a project team.​ In this module, we will introduce the simplex method for solving LP problems.

Earlier, we demonstrated the simplex method on a LP that is in a standard form, i.e., the problem is maximization, all functional constraints are "≤" inequalities, and all variables are non-negative. However, it is very rare that a real-world problem is in a standard form. How, then, do we solve problems which are in non-standard forms? Instead of developing many variations of the simplex method, where its steps depend on each particular type of non- standard form, we transform the problem to the standard form and use the same simplex algorithm without any change in its rules.