The Simplex Algorithm

1
The Simplex Algorithm

• An Algorithm for solving Linear Programming
  Problems

2
We Start with a Linear Programming Problem

• Maximise P 4x 5y 3z
• Subject to the constraints
• 8x 5y 2z ? 4
• x 2y 3z ? 1

3
Setting up the Tableau

• First rearrange the equation for P so that it is
  equal to zero
• P - 4x - 5y - 3z 0

4
Introduce Slack variables

• 8x 5y 2z ? 4 becomes
• 8x 5y 2z s 4
• x 2y 3z ? 1 becomes
• x 2y 3z t 1
• s and t are called the slack variables

5
This is the Tableau (Fancy word for table)
6
Finding a pivot

• Chose any negative number in the first row
• Consider the positive values in the column below
  it
• Divide the value in the last column by the
  corresponding value in the chosen column and see
  which gives you the least
• That tells you which is the pivot...it goes like
  this

7
4/8 1/2 1/111/2 is the least so 8 is the
pivot

8
The next step is to reduce the pivot to 1 by
dividing equation