The Two Stage Simplex Method

A quick guide to how to use the Two Stage Simplex algorithm which is used for problems involving "greater than or equals to" constraints, from the Decision Maths course. Whilst this is written with the Edexcel 2017 syllabus in mind, it is suitable for other courses. All other algorithms and procedures for the course will have their own videos too.
Original Simplex Algorithm video:
• The Simplex Algorithm
Playlist for Decision Maths Algorithms and Procedures: • Decision Maths Algorit...
Music: Temporary Escape - MaxMiecchi, available from tribeofnoise.com.
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[@bulldogwuffwuff1642]

my brain when simplex

[@Charles_Reid]

Checking the vertices of the convex octagon I see. You’re catching on!

[@PunmasterSTP]

Tableau? More like tabl-oh yeah, because this video was awesome; thanks for posting it!

[@mathshelpwithmrorys8555]

Ha ha. Thanks for the great comment! I'm glad it was useful to you.

[@PunmasterSTP]

@@mathshelpwithmrorys8555 You are most welcome, and I can keep those kinds of comments up if you'd be interested...

[@daniniamut1362]

I don't get it, can you explain?

[@PunmasterSTP]

@@daniniamut1362 No problem. "Tableau" is another term that's used to refer to the matrix of coefficients in the simplex method.

[@huichen6461]

Great demonstration

[@mathshelpwithmrorys8555]

Thank you!

[@Isabellaa-ms5dk]

this video is the best... thank you so much for saving my grade!!!

[@realcirno1750]

THANKS FOR THIS!!!

[@mathshelpwithmrorys8555]

You're welcome. I'm glad it was helpful to you.

[@mlpnkobjiv]

Your voice is amazing 💕 Can you also make a video about post optimality analysis??

[@steelboy1164]

Man saved my exam

[@alimurtaza890]

thank you

[@mathshelpwithmrorys8555]

You're welcome.

[@birgirjohannesjonsson5434]

Great explanation. Thank you :)

[@matheussoffiati2944]

Whats the purpose of minimising artificial variables? I dont understand the link between minimal artificial variables and a feasible solution

[@Xcess007]

we introduced them to be able to solve it with SIMPLEX. They should be zero if we want a real-world answer.
Another way you can look at it is this:
You extend the feasible region to include the (0,0) region up to it (so you can use simplex), then you minimize artificial variables first to get out of that zone and get to the real feasible zone. Then stage 2 starts and you can move around the corners to find the best solution.

[@xKibz]

So if "I" equals the negative sum of artificial values, if there is one artificial value will "I" equal -(a1) ? and if there is three artificial values will I = -(a1 + a2 + a3) ?

[@mathshelpwithmrorys8555]

Yes, absolutely!

[@timelygoose]

Thank you sir

[@navzz2678]

is it possible to have a value of 0 for the I row but still have negative values? if so would you just continue until there are no more negative values in the I row ?

[@mathshelpwithmrorys8555]

Yes, it is possible. Once the I row has a value of 0, we have a basic feasible solution, remove the I row, and the artificial variable columns, then move into the second stage.

[@othusitsemolokele4659]

So if it was a maximise problem the we'd just work with P? No need to set it to something like with example

[@abanoubmagdy974]

this vid is outstandingly easy to follow and comprehend huge thanks !! Question which text book follow this methodology ?? as I've been following along with professor Hamdy Taha's Book of OP Research
Thanks Again :) .

[@theavocado7296]

This is primarily focused for students who are taking A-level further Maths, it is present in the Edexcel Decision 1 textbook chapter 7

[@Sam-yr9gf]

2:00 how is it possible for x and y to be 0, wouldn't that violate the constraint?

[@ratofalady8125]

Is I always being set up to be minimising so always -(a1 + a2)

[@mathshelpwithmrorys8555]

Yes, exactly that.

[@ratofalady8125]

@@mathshelpwithmrorys8555 so you can never be given a maximising problem that includes I ?

[@ratofalady8125]

@@mathshelpwithmrorys8555 so you can never be given a maximising problem that includes I ?

[@mathshelpwithmrorys8555]

@@ratofalady8125 No, that is not the case. You will have to use the standard methods for dealing with a maximising and minimising problem and combine that with I. If you are unsure about how to approach maximising, please watch my video which has both maximising and minimising. ua-cam.com/video/t0NkCDigq88/v-deo.html

[@jamesmcgurrin8160]

how do you use I if it's for a maximisation question? Thank you

[@jamesmcgurrin8160]

is it just I = (a1+a2) ?

[@SamAX5444]

It wasn’t clear how you picked the basic variables?

[@othusitsemolokele4659]

The columns with only1's and 0's are your basic variables

[@SamAX5444]

@@othusitsemolokele4659 for the basic var. column when constructing the first tableau 3:07