# Chapter 7 The Simplex Algorithm Flashcards

How do you demonstrate that your solution is feasible?

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

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

You get these by reading off the values from your tableau

Eg the

How do you show that your solution is optimal?

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

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

What do you do if a theta value is undefined?

Ignore it

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

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

What is a slack variable?

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

What is the first step when doing simplex?

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

What does an initial tableau look like?

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

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

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

How do you calculate theta values?

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

Value/pivot

Why are the theta values useful?

They enable you to determine the pivot row

The pivot row is the row with the smallest theta value

Why is the pivot row important?

You will then / that row by the pivot value

What do you never do when selecting theta values?

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

What do you do after you have the pivot row?

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

What is the quick way to determine the row operations

The first row operation will be Rp/pivot value

The others will be Rx+- the values in the associated pivot spot

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

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