Chapter 7

Question 1

Outline basic simplex

Answer 1

1. make & rearrange constraints to eqns
2. create initial tableau
3. select column with most -ve value
4. value column / pivot column for all rows
5. smallest +ve value is pivot element & row
6. manipulate to make pivot element 1
7. +/- multiples of pivot row to other rows to make next tableau
8. continue until no negatives in P row

Question 2

Outline 2 stage simplex

Answer 2

1. make & rearrange constraints to eqns
2. let I = - (sum of artificial variables)
3. rearrange to isolate value
4. create initial tableau and carry out simplex
5. remove I row and artificial columns when no negative in I row
6. continue with basic simplex until no negatives in P row

Question 3

Define M

Answer 3

arbitrarily large number

Question 4

Outline big M simplex

Answer 4

1. make & rearrange constraints to eqns
2. isolate artificial in artificial equations
3. -(M x artificial) from objective function
4. rearrange to isolate constant
5. insert into tableau
6. carry out basic simplex until no negatives in P row

Question 5

Outline how to minimise a function

Answer 5

Maximise the negative