Linear Programming (Optimization) 2 Examples Minimize & Maximize

Learn how to work with linear programming problems in this video math tutorial by Mario's Math Tutoring. We discuss what are: constraints, feasible region and the objective function. We go through 2 examples one involving finding the minimum for an unbounded region and the other a word problem example involving maximizing profit for a bounded region.
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Another Linear Programming Video I did here:
• Linear Programming
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[@AA-yk8zi]

You really are making learning math less stressful! Thank you!

[@134princesa]

Oh my God, thank you. I am an accounting student and have to take a Management Science course, but I have always struggled with math all my life. Just following book instructions is hard for me, I have to see the steps for how to solve them. I understood everything with you, thank you so much. Proffesors like you make the classes easier, even math.

[@MariosMathTutoring]

You’re welcome! I’m glad the video helped you understand linear programming.

[@LazaretFet]

I have a project on linear programming so this is like a GODSEND for me as none of the 10th grade textbooks ever covered this and there nothing on the net as well so thank you Mario you're the best.

[@morganstaff5761]

Thank you so much for this. I was not understanding this at all in my class and getting so upset until I watched this video and it all clicked. I’ve done 3 problems since watching this and gotten them all right

[@empyrean5330]

Thank you! I had a vague grasp of linear programming concepts but these lectures are helping me build a solid foundation to learn from.

[@ExpertPlum]

honestly saved my life, 1 hour before Uni assignment was due found this video which helped me so much

[@alex-em4em]

I can't believe this was actually so easy! Thank you Mario!

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[@MariosMathTutoring]

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I was stuck with the x ≤ 2y part during my exam because my instructor never taught us that you can graph it like that, I swear man your math tutorials are the best!

[@MariosMathTutoring]

Glad my video helped you! You can always graph inequalities using slope-intercept form by solving for y.

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You have helped me beyond belief. Thank you for making math interesting dude.

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[@MariosMathTutoring]

Best of luck!

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Hope you're feeling better now and good luck with your studies!

[@SlickMK2]

I'm in BNAL 306, this really helped it click for the first time, thanks.

[@MariosMathTutoring]

You’re welcome! Glad it helped you.

[@Nobars-z1q]

We never did this in class, when I saw it in a past exam paper, I was like what in the world!!! , I need to check Mr Mario, thank you so much.

[@nidhi_prem]

This was such a clear and simple explanation!!! TYSM

[@aaroncheri]

Thank you, Mario. You have explained the constraint optimization problems well. I learned a lot from you. God bless.

[@MariosMathTutoring]

Glad to help!

[@michaelfelix6460]

Thanks been struggling with linear programming for a while now, finally getting the hang of it.😊

[@MariosMathTutoring]

Glad I could help!

[@melindamutoro6879]

of all the tutorials l have seen today you are trhe only one that made my life easier, thank you soo much

[@mmmdonutsss]

Thank you so much. I’m struggling so much and this really helped ! Do you offer live tutoring ?

[@MariosMathTutoring]

Glad my video helped you! You can find out about my paid tutoring here: www.mariosmathtutoring.com/online-math-tutoring.html

[@sultanharebalsuwaidi9830]

The way you explain things is so out of this world. Thanks

[@MorganPETERApa]

Thank you for giving us a simplified understanding of the concept of linear optimization.

[@MariosMathTutoring]

Glad it was helpful!

[@sarojmajhi7182]

This vid was helpful ❤❤

[@kentaro2812]

Only video that helped me understand the min max concept for my honors algebra 2 class online!

[@DidintleMoleko]

This was extremely helpful, my lecturer made it so complicated and lost me and the textbook wasn't helpful at all. Thank you

[@MariosMathTutoring]

Glad it helped!

[@landon_arsen]

Thank you so much, I appreciate your video! you just saved my life because I didn't understand any of this.

[@MariosMathTutoring]

You're welcome! I'm glad my video helped you understand linear programming.

[@freefallfn]

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[@MariosMathTutoring]

Awesome! Thanks!

[@MTXMTX-oj6yn]

Thanks a lot :it's still always better to build up the whole equation , write it down ;before proceeding .thanks again

[@MariosMathTutoring]

I'm not sure what you mean about "building up the whole equation" but glad to hear you liked the video.

[@rosanasanches641]

finally a real teacher uff!! thank you !🙌

[@denelhorn4992]

Notice that the profit for road bikes would be 15x200y= 3000. I would definitely make more road bikes. Thank you very much for an awesome video.

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U are really amazing teacher

[@llyvm]

I was struggling on a homework problem and this really helped. Thank you so much.

[@MariosMathTutoring]

Glad it helped!

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You're the best sir. I hope my professor will teach us like that 😭

[@MariosMathTutoring]

Thanks, I'm glad you liked the video!

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[@MariosMathTutoring]

Glad it helped!

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[@MariosMathTutoring]

Thank you!

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[@MariosMathTutoring]

You’re welcome! I’m happy to hear that my videos help with your Honors Algebra 2 class.

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[@MariosMathTutoring]

Glad to hear that

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[@MariosMathTutoring]

Glad it was helpful!

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Wtf😂

[@ahmetpehlivan3698]

Clean and nice lesson, Thanks sir.

[@chrisfrshw]

@ mario great video.. my question is (and hoping you can point me to some material) in the example you used we were trying to optimise the production vs profit equation. How would these same principles/method work where im trying to optimize/solve a profit equation based on a demand function where price / demand relationship is linear (or non linear) and the profit equation is dynamic based on the price setting. I really struggle to grasp this. Thanks in advance.

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This guy is a legend

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[@MariosMathTutoring]

Appreciate it!

[@amusimakuhle2011]

Thank you so much, this is exactly what I needed to jog my memory.

[@maxmacalupu5336]

Wonderful explanation.

[@sxint.nineteen1751]

THANK YOU SO MUCH i have a final tomorrow and was stressed about this using a TI-84 makes me all confused THIS IS GREAT THANK U THANK U 🙏🏻🙏🏻

[@swatityagi222]

Hi Mario, Can you upload more videos on convex optimization problems covering duality ?

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May God bless you and live longer to share your Knowledge

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You really helped me out with this prof thanks

[@pravinkumar54]

Hi mario, Great video. Where can i find more exercises and your resource materials for the same?

[@StAnnsGirlsSHSSampaGhanaBonoRe]

This video helped a lot to understand linear programming. have you uploaded more videos on youtube or other channels? I want to follow

[@dawneabdulal-bari9313]

Awesome presentation ~ Thanks

[@MariosMathTutoring]

Glad you enjoyed it

[@davidsiff]

Amazing explanation, but what do you do when you have more than two variables and can’t put them on a two dimensional graph?

[@sierrabarajas4220]

Your videos always help me. Thank you!

[@MariosMathTutoring]

Glad my videos are helping you!

[@user-ug6kq7cq8s]

didnt you do a mistake for having twice as many mountain bikes as road bikes? since mountain bikes is X, wouldnt it be 2X=>Y? (2X greatear than or equal to Y)

[@ogunleyeaderinola1663]

I thought so too that he made a mistake

[@ogunleyeaderinola1663]

okay so i just realized that he didn't actually make a mistake . twice as many as A as B is the same as A is twice as many as B

[@madonnasplasticsurgery]

Same, it’s just a weird way of writing the constraint. You can have X have a higher value than Y • 2 of anything and it would still work, X being greater. I definitely would’ve written it differently tho.

[@augustinechidexnnamah2023]

Hey over there, he was actually right! Twice as mountain bikes as road bikes means the mountain bike should be equal to two times the road bike

[@daviesDynamo7554]

good morning sir. this is my first to see your videos and you really getting me started. i am really struggling on an assignment. please help.

[@arouneselvalingampanneerse6836]

Very nicely done .. It was easy to understand . Thanks very much

[@user-ol6xw4te8j]

Excellent job!

[@eliandruh9084]

Hello! What if the coordinates on both my subjective functions turn out to be the same?

[@MrAHariharan]

Sir. What if there are 3 equations instead of two? It is easier to solve two equations using elimination method or substitution method. But I have no idea how to solve if there are three different inequality equations. If you have any link regarding this, then kindly share it. Thank you

[@evansiegel1732]

In simple terms, you'd have three lines and there would be more than three points of intersection. So you would use the same techniques (graph, find the feasibility region, find the coordinates of the intersection of the graphs which border the feasibility region, and plug these coordinates into the function you're trying to maximize or minimize). Hope that helps!

[@keylialano]

what if there's no processing time or production time? is it okay to have same constant but different time available? Like a+b

[@didigarcia8825]

this was soo helpful. Thank you

[@MariosMathTutoring]

Glad it was helpful!

[@sonnybattaglia4760]

So useful! Thank you.

[@omranlootah9979]

Amazing teach 💯

[@benjamin13212]

In the word problem, wouldn't the second inequality be 2x >= y, not the other way around? The constraint is at least twice as many mountain bikes (x) as road bikes (y)

[@sewnetatewu8958]

thanks a lot..... u really make maths easy

[@itscrewston6684]

So you can use substitution for minimization and maximization? Can you do the same using the simplex method?

[@patriciachuka9371]

Very nice and on point explanation. Keep it up💪

[@mr.v9083]

Sir, that was really very much helpful for me. I have a few more question so can you please tell me how can I ask you those questions. It will be so nice of you if you help me.

[@shanejhang997]

For the first question, why it is the (2,3)? why cannot be some other points on the edge?

[@dinushenya2026]

please explain what about 3 constraints how to find the intercept

[@acerella7217]

thank you so much Sir! God bless you

[@ukaszmilunas4850]

I love it. Thank you!

[@MariosMathTutoring]

Glad you like it!

[@OMGitsjustperfect]

Why only test intersection points? In a more complicated linear system with a more complicated objective function you should go through the entire space no?

[@MichalVano]

this is exactly my question and i am not sure why no one mentioned this. Did you figure it out?

[@beecrofttobiloba1869]

Thank you sir God bless❤️

[@melodydeng6599]

thank you so much, sir, absolutely helpful

[@toymonster7544]

Thanks this helped me a lot! :)

[@JOLINJTURKCS]

awesome explanation

[@vlogsbySapna]

Sir if we have had a value x and y is 0 then how we will make the graph ? When both x and you =0 then how we will make the graph?

[@EliasMasikaPhD]

which side are you shading? the required or the unwanted region?

[@omertop8131]

thank you Mr.Mario

[@anymorechangara7146]

That's very good do not miss it

[@niyucoa]

multumesc domnule lamatic nu vad ziua de maine!

[@khantzarni9326]

May I ask why when the equation has ">=" or "

[@mynameisnothere6978]

I believe plain greater than or less then are dotted. while less then or equal to or greater then or equal to are solid. Good luck

[@mohitpatel1536]

Thanks! U r awesome

[@jaydaka7886]

That was really helpful thanks

[@angelacreed9806]

Thank you so much for this Sir!

[@makaemakhotla5922]

How do we confirm that a point is indeed a maximum point since we gave an unbounded region

[@brianv5666]

finally understood it!

[@sarasultan1745]

it helps me a lot thanks so much ❤️

[@zimasajam]

Really good😄

[@MariosMathTutoring]

Thank you so much 😀

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This can help me I'm doing ncv level 3?

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You are a good man