Chapter 7 The Simplex Algorithm

Question 1

How do you demonstrate that your solution is feasible?

Answer 1

You sub your values into all of your equations (including your restraints)

Question 2

What are the final set of equations given by your tableau?

Answer 2

You get these by reading off the values from your tableau
Eg the

Question 3

How do you show that your solution is optimal?

Answer 3

You write the equation so that profit is the subject of it
Then you can say that increasing/decreasing them would clearly lead to a higher or lower value of P

Question 4

What is the simplex tableau algorithm (don’t learn it just roughly know it)

Answer 4

Question 5

What do you do if a theta value is undefined?

Answer 5

Ignore it

Question 6

After formulating a linear programming model what is the preliminary step to setting up a simplex problem?

Answer 6

Introducing slack variables into the constraints where the slack variables are also positive

Question 7

What is a slack variable?

Answer 7

Since we don’t know the actual solution the slack variables represent the difference in the rreal and changed value by creating the equations

Question 8

What is the first step when doing simplex?

Answer 8

You write your objective function =0 with the P being +

Question 9

What does an initial tableau look like?

Answer 9

On the y axis you have your slack variables and on the bottom the P/Q
On the x axis you have all the variables with the value on the end
You then dill in each constraint in the tableau inputing 0 when there isn’t that variable
The objective function goes on the bottom

Question 10

What do you do after you have filled in the tableau?

Answer 10

You can the bottom row for the most negative number to find the pivot column
Then circle this column
Then you need to calculate the theta values for each row. This is done by:
The term in the value column / the term in the pivot column

Question 11

How do you calculate theta values?

Answer 11

The term in the value column / the term in the pivot column
Value/pivot

Question 12

Why are the theta values useful?

Answer 12

They enable you to determine the pivot row
The pivot row is the row with the smallest theta value

Question 13

Why is the pivot row important?

Answer 13

You will then / that row by the pivot value

Question 14

What do you never do when selecting theta values?

Answer 14

You get no marks for selecting a negative or 0 theta value

Question 15

What do you do after you have the pivot row?

Answer 15

As mentioned before / by the pivot value
Then you want to make it so that the the other values in that row are 0.
You are trying to get a 1 in the pivot value and 0 in the others
You need to show your row operations and they are aways in reference to pivot row

Question 16

What is the quick way to determine the row operations

Answer 16

The first row operation will be Rp/pivot value
The others will be Rx+- the values in the associated pivot spot

Question 17

What have you reached your optimal solution in the simplex tableau?

Answer 17

Once all of the values in the objective (profit) row are positive

Question 18

What row do you not calculate a pivot value for?

Answer 18

The objective row (profit)

Question 19

How do you do simplex if you are trying to minimise losses?

Answer 19

Define Q to be -P then use the same method

Question 20

How do you read off your answers from a completed simplex tableau?

Answer 20

You look at your basic variables (the y axis) then look. At the value that they are. Anything that is not a basic variable is 0.

If you are minimising the problem remember that the Q=-P

Question 21

How do you find the new constraints and objective value after doing the simplex tableau?

Answer 21

You just read them off the tableau

Question 22

How do you prove that the simplex tableau’s values are optimal?

Answer 22

Write P as the subject and then show that an increase in any of these values will lead to an increase/decrease in P

Question 23

What is a very tricky question that the mixed exercises asked?
Why was it tricky?

Answer 23

State the 5 constraints
x,y,z>0 counted a 3

Question 24

What can you never so with the objective function?

Answer 24

Simplify it

Question 25

How do you show what the pivot column and row it?

Answer 25

You circle the pivot column then you circle the value in that column which is in the pivot row

Question 26

How did I improve my previous method for finding whole integer solutions?

Answer 26

You can set up the whole thing at once on the calculator

Question 27

What do you never want to forget?

Answer 27

The unit in the end of an answer
The constant of integration
Rounding stated in the answer

Question 28

What may the question not tell you to do but expect you to do?

Answer 28

Find integer solutions

Question 29

What are the 2 other simplex methods called?

Answer 29

2 stag simplex method
Big M

Question 30

What do you. Do with ≥ constraints?

Answer 30

Subtract a surplus variable s (s,a≥0)
Add a artificial variable

Question 31

Why do we need a artificial variable (non official reason)

Answer 31

When x any y are basic variables equal 0 then s would be negative

Question 32

What is visually different in the 2 stage simplex method?

Answer 32

You have artificial variables
And you have a new I row

Question 33

What does I equal?

Answer 33

The sum of the artificial variables X-1
I=-(a1+a2)

Question 34

What is the first actual simplexy step in the 2 stage simplex method

Answer 34

You do normal simplex but on the I row instead (you still have I or P as the objective function)

Question 35

When can you do the second stage of the 2 stage simplex method?

Answer 35

After all the variables in I are positive you have a feasible basic solution
You can continue if the I value is 0 (a has been minimised)

Question 36

How do you start the second stage of the 2 stage simplex method?

Answer 36

You use the same simplex tabula but get rid of the I and all the a’s and continue as normal simplex

Question 37

How is the big M method different?

Answer 37

After converting to slack, surplus and artificial variables you subtract M lots of the sum of the artificial variables from the objective function (before you change it so i t will end up becoming a +)

Question 38

What is the significance of M within the tableau?

Answer 38

It is an arbitrarily large constant

(Learn exact)

Question 39

How do you show that a theta value is negative?

Answer 39

-ve (don’t just cross it out)

Question 40

How do you minimise a function with the big M method?

Answer 40

Same as usual let Q=-P

Question 41

What is a common mistake when minimising?

Answer 41

Forgetting to change back your answers to the Q=-P

Question 42

When do you do the big M bit?

Answer 42

After everything else is done.
There is no difference, it will always be -Ma

Question 43

What are the 3 algorithms in this section?

Answer 43

Simplex algorithm
2 stage simplex algorithm
Big M simplex algorithm