The Student Room Group

D1 - Simplex method....is this possible to understand????

I know there have been previous threads about this but i'm really struggling with understanding wot the hecks going on for the simplex method....I can't even seem to follow a systematic/step by step approach to it because the book is rubbish at explaining it....

Does anyone know of any sites which give good explanations? Or does anyone know of a step by step procedure to follow when solving a simplex table???

Any help is much appreciated

Thanks

Dake
Reply 1
You should look up "Gaussian Elimination" - it's not exactly the same thing, but I have a feeling that's what simplex is based on - it certainly helped me when I was doing D1...
Reply 2
Briefly:

(1) Put the inequalities and objective function in standard form by adding slack variables and writing the objective function in the form P-..........=0

(2) Form the intial tableau.

(3) Select the most negative entry in the objective row.

(4) Consider the column that corresponds to the most negative entry. Calculate theta values [(value)/(column)] for each row other than the objective row and choose the smallest.

(5) The pivot lies at the intersection of the row with the smallest theta value and the column with the most negative entry in the objective row. Circling the pivot. This variable (eg x,y,z) at the top of the pivot column is called the entering variable while the slack variable (eg r,s,t) at the far left of the row of the pivot is called the leaving variable. In the new tableau the entering variable replaces the leaving variable.

(6) Divide all entries in the pivot row by the pivot.

(7) Consider a row other than the pivot. You need to add a suitable multiple of the value of the pivot box(which is now 1, as you divided the pivot row by the pivot) to the value in the pivot column of the row being considered so as to make the entry 0.

(8) Working your way along the row being considered, add the SAME multiple as before of the value from the pivot row, but you're adding multiples from the column of the pivot row corresponding to the column in the row being considered. Repeat until the row being considered is now finished.

(9) Repeat (7)+(8) for all rows other than the pivot row.

(10) The tableau has been revised. If there are no negative entries in the objective row the process is complete and you can interpret the results. If there are negative entries then i'm sorry but you have to repeat (1)-(10).

Hmm. Looking back that doesn't seem that brief. Feel free to ask about what you're unsure of.
Reply 3
Gaz031
Briefly:

(1) Put the inequalities and objective function in standard form by adding slack variables and writing the objective function in the form P-..........=0

(2) Form the intial tableau.

(3) Select the most negative entry in the objective row.

(4) Consider the column that corresponds to the most negative entry. Calculate theta values [(value)/(column)] for each row other than the objective row and choose the smallest.

(5) The pivot lies at the intersection of the row with the smallest theta value and the column with the most negative entry in the objective row. Circling the pivot. This variable (eg x,y,z) at the top of the pivot column is called the entering variable while the slack variable (eg r,s,t) at the far left of the row of the pivot is called the leaving variable. In the new tableau the entering variable replaces the leaving variable.

(6) Divide all entries in the pivot row by the pivot.

(7) Consider a row other than the pivot. You need to add a suitable multiple of the value of the pivot box(which is now 1, as you divided the pivot row by the pivot) to the value in the pivot column of the row being considered so as to make the entry 0.

(8) Working your way along the row being considered, add the SAME multiple as before of the value from the pivot row, but you're adding multiples from the column of the pivot row corresponding to the column in the row being considered. Repeat until the row being considered is now finished.

(9) Repeat (7)+(8) for all rows other than the pivot row.

(10) The tableau has been revised. If there are no negative entries in the objective row the process is complete and you can interpret the results. If there are negative entries then i'm sorry but you have to repeat (1)-(10).

Hmm. Looking back that doesn't seem that brief. Feel free to ask about what you're unsure of.



That's fantastic!!!!!thanks alot! Will try a few questions using this method and get back to u if any problems occur.

Thanks again!

Dake
Reply 4
Gaz's procedure is good.

If you want a website, try

http://www.colchsfc.ac.uk/maths/simplex/simplex_intro.htm

For the purely Edexcel-Heinemann method, go to

http://www.colchsfc.ac.uk/maths/simplex/Edexcel/edexcelsimp.htm

Aitch
Reply 5
Gaz031
Briefly:

Hmm. Looking back that doesn't seem that brief.


This is the problem, isn't it? It's not brief!

That's why it didn't appear on the D2 paper. You need to cut out 2 other questions to make time for it!

Aitch