MWA - Simplex Method

One Stage Simplex

Convert inequalities to equations using slack variables

Choose pivotal value

Divide row by pivotal value and subtract from other rows in order to get all 0s in pivotal column except for a 1 in pivotal row

One Stage - How to convert inequalities <= RHS?

… + … + s = RHS

One Stage - Which value is chosen for pivotal column?

Most negative value in objective function row

Ratio Test

For each row:
RHS / value in pivotal column

One Stage - Which value is chosen after ratio test?

Smallest non negative value (including 0)

When is one stage optimal?

No negative values in objective

Two Stage Simplex

Convert inequalities to equations using slack and artificial variables

Calculate Q

Choose pivotal value

Divide row by pivotal value and subtract from other rows in order to get all 0s in pivotal column except for a 1 in pivotal row

Two Stage - How to convert inequalities <= RHS?

… + … + s = RHS

Two Stage - How to convert inequalities >= RHS?

… + … - s + a = RHS

Two Stage - How is Q row calculated?

Rearrange each row for each artificial variable

Q = sum of all artificial variables

Two Stage - Which value is chosen for pivotal column?

Most positive value in artificial function row

Two Stage - Which value is chosen after ratio test?

Smallest non negative value (including 0)

When is two stage complete?

Q = 0 or all variables in Q row are positive or zero

After two stage complete?

Reduce table by removing Q row and artificial columns

Start one stage simplex