# Chapter 7 The Simplex Algorithm Flashcards

1
Q

How do you demonstrate that your solution is feasible?

A

2
Q

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

A

Eg the

3
Q

How do you show that your solution is optimal?

A

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

4
Q

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

A
5
Q

What do you do if a theta value is undefined?

A

Ignore it

6
Q

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

A

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

7
Q

What is a slack variable?

A

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

8
Q

What is the first step when doing simplex?

A

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

9
Q

What does an initial tableau look like?

A

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

10
Q

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

A

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

11
Q

How do you calculate theta values?

A

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

12
Q

Why are the theta values useful?

A

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

13
Q

Why is the pivot row important?

A

You will then / that row by the pivot value

14
Q

What do you never do when selecting theta values?

A

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

15
Q

What do you do after you have the pivot row?

A

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

16
Q

What is the quick way to determine the row operations

A

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

17
Q

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

A

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

18
Q

What row do you not calculate a pivot value for?

A

The objective row (profit)

19
Q

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

A

Define Q to be -P then use the same method

20
Q

A

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

21
Q

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

A

You just read them off the tableau

22
Q

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

A

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

23
Q

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

A

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

24
Q

What can you never so with the objective function?

A

Simplify it

25
Q

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

A

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

26
Q

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

A

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

27
Q

What do you never want to forget?

A

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

28
Q

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

A

Find integer solutions

29
Q

What are the 2 other simplex methods called?

A

2 stag simplex method
Big M

30
Q

What do you. Do with ≥ constraints?

A

Subtract a surplus variable s (s,a≥0)

31
Q

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

A

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

32
Q

What is visually different in the 2 stage simplex method?

A

You have artificial variables
And you have a new I row

33
Q

What does I equal?

A

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

34
Q

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

A

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

35
Q

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

A

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)

36
Q

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

A

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

37
Q

How is the big M method different?

A

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 +)

38
Q

What is the significance of M within the tableau?

A

It is an arbitrarily large constant

(Learn exact)

39
Q

How do you show that a theta value is negative?

A

-ve (don’t just cross it out)

40
Q

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

A

Same as usual let Q=-P

41
Q

What is a common mistake when minimising?

A

42
Q

When do you do the big M bit?

A

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

43
Q

What are the 3 algorithms in this section?

A

Simplex algorithm
2 stage simplex algorithm
Big M simplex algorithm