Solving Linear Programming Problems Using Simplex Method

Solving Linear Programming Problems Using Simplex Method-2
For example, given the constraint from the linear program.In this way, all lower bound constraints may be changed to non-negativity restrictions.

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George Dantzig worked on planning methods for the US Army Air Force during World War II using a desk calculator.

During 1946 his colleague challenged him to mechanize the planning process to distract him from taking another job.

It can be shown that for a linear program in standard form, if the objective function has a maximum value on the feasible region, then it has this value on (at least) one of the extreme points.

This in itself reduces the problem to a finite computation since there is a finite number of extreme points, but the number of extreme points is unmanageably large for all but the smallest linear programs.

First, for each variable with a lower bound other than 0, a new variable is introduced representing the difference between the variable and bound.

The original variable can then be eliminated by substitution.

Dantzig later published his "homework" as a thesis to earn his doctorate.

The column geometry used in this thesis gave Dantzig insight that made him believe that the Simplex method would be very efficient.

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