The Simplex Method

The previous lesson completed our knowledge of pivoting. We know how to choose the entering and leaving variables to maximize the objective function. The only missing piece of information is when do we stop? This question will be answered in the exercises, but first, it is time to practice the simplex method. Here is the original linear programming problem.

Maximize z = 4x1+3x2
Subject to:2x1+x2£40
x1+x2£30
x1 £15
wherex1andx2³0

Slack variables, x3, x4, and x5, have been introduced into the constraints. The initial simplex tableau is shown below. It is up to you to calculate the quotients when needed. Have a pencil and some paper handy.

Solve this problem using
the simplex method
Basic x1 x2 x3 x4 x5 z RHS Leaving
x
x
x
z
Entering

Exercises

  1. How do you know when to stop?
  2. What happens if there are no positive quotients but there are still negative indicators?

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