Linear Programming: Blending/Mixing with Excel Solver (Flexible Recipe)

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How to combine/mix together a given set of inputs (e.g. raw materials) to create outputs (e.g. final products) in a way that optimizes an objective (e.g. profit) and obeys constraints on material availability, quality of the final products, and production requirements? In this example, we consider the case where the final products are made according to a flexible recipe. The fixed-recipe version of this video can be found here: • Linear Programming: Bl... .

[@SeanWyatt-h6f]

Thank you! I did not even know that I was trying to solve a flexible variable problem until I saw you define it. That is staying in my toolbox.

[@TallysYunes]

Excellent!

[@tbirdspy8911]

This was a huge help completing my homework assignment in time. Thank you!

[@TallysYunes]

You're welcome!

[@tubuddcfo5833]

thanks a lot for the linearisation tip! I was struggling with my assignment and didn't understand why it didn't work, now I know how to resolve it. Also the way that you explained different types of the problems in your videos is very easy for new learners to categorise the problems and sort out how to solve it. So helpful!

[@TallysYunes]

You're welcome. Glad it was helpful.

[@avtarsinghmatharu1061]

Wonderful examples explained in a logical and simple way.

[@TallysYunes]

Thank you for this kind compliment! I'm happy to hear you liked the video!

[@lebzgold7475]

This is the BEST explanation of a flexible blending problem. Thank you so much. New subscriber here.

[@TallysYunes]

Thank you so much! I appreciate your subscribing! Glad the video was helpful.

[@ivanponce9317]

It looks so easy when its done wow. Thank you for your work!

[@TallysYunes]

Glad it was helpful.

[@JohnFerrante-ep3jw]

dude! I just enrolled in a mba and they have me doing linear optimization. The initial problems weren't bad, but it just seriously kicked up a notch. Would really appreciate if I could send you this one problem in particular and see how you would approach it.

[@TallysYunes]

I can't do homework for you, but it's likely that the one you need to tackle is similar to one of the examples in my videos. Look through my Excel Models playlist.

[@JohnFerrante-ep3jw]

@@TallysYunes of course not! I'll be sure to check out the videos. I'm struggling with determining if it's blending or allocation, and determining the inequalities for blending. Especially when there's multiple rates and units of measurement. Do you offer tutoring?

[@TallysYunes]

At the moment I don't have time for one-on-one tutoring, but this is something your teacher would be able to clarify for you (it's their job). Have you tried reaching out to them? Do they offer office hours?

[@savannahballard9992]

Thank you this was very helpful.

[@TallysYunes]

You're welcome!

[@bdobin8]

thank you , really helped out

[@TallysYunes]

You're welcome! Glad it helped!

[@patricksydow4266]

Very well explained. I would like to see one with cost minimization.

[@TallysYunes]

Thanks! You could simply remove the revenue portion from the objective function, delete the negative sign in front of the cost portion, and switch the "max" to a "min." That's it!

[@jayzeen]

Can you tell me how to tackle this kind of problems when the components have a specific range of amount to be used(As an example - S should contain atleast 2 gallons of component 1 and atmost 5 gallons of component 1)

[@TallysYunes]

You just add two more constraints. In my gasoline example: C1S >= 2 and C1S

[@jayzeen]

@@TallysYunes I had a feeling it might be something like this but wasn't sure .. Thanks a lot❤️

[@evionlast]

How can we detect problems in the constraints of this type of blending problems?, can you give a textbook reference on the subject?

[@TallysYunes]

What do you mean by detect problems in the constraints? Determining whether or not a constraint is correct is equally difficult for all kinds of problems. It takes practice. There are several good books on modeling. One of them is "Model Building in Mathematical Programming" by H. Paul Williams.

[@evionlast]

@@TallysYunes so there's no heuristic to find if the constraints are making the problem unfeasible or trivial? Suppose you have a number of n blendings, if the constraints are too loose would there be overlap in the blendings such that blend m is similar or equal to blend n, and the problem is unfeasible, is that why there's redundancy en the constraint matrix, what would be the clue if that is so, or am I completely wrong? How would I understand that from the constraint matrix. Sorry for the convoluted question...

[@evionlast]

I'm self studying so that's why I took myself down this labyrinth ... Thanks 🙏🏼

[@TallysYunes]

Your question makes sense. Finding a constraint or set of constraints that are responsible for the infeasibility of a problem is an entire field of study in itself. There have been doctoral theses published on this. Depending on the problem type, it may be easier or harder. In general, it's not trivial. Some commercial solvers try to do this automatically and also try to detect redundant constraints automatically to delete them.