How to Solve a Linear Programming Problem Using the Graphical Method
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- เผยแพร่เมื่อ 20 ต.ค. 2024
- In this lesson we learn how to solve a linear programming problem using the graphical method with an example. We also see an example for an in-feasible LP.
This video is HD, and Close Captioning is available.
This was the BEST explanation I've experienced. Took you 11 minutes what my graduate professor couldn't make clear in over 3 hours. THANK YOU
We must have the same professor hahahaha
@@mikalbrown3227 For Real man
It is because they teach us, as we are their professors friends.
It's incredible how ten minutes of well explained lecture are better than weeks in class. Awesome video!
It's been over 5 weeks since the class started, but all I know was nothing til I met you 15 min ago! I AM LITERALLY AMAZED !! Thanks a lot!
😑😑
The choice of Z is arbitrary, but we usually choose a Z value that gives us a line in the feasible region. I picked 60 only bcz its divisible by 3 and 2 and give me a line inside the feasible region. you could have selected other values such as 50 for your first line. However, for the second line, it is important to pick a value that is consistent with the objective function direction. i.e. for a max problem pick a bigger value, and for a min problem pick a smaller value than the first value. I could have chosen 100 instead of 120 and still get the right direction for the objective function improvement. Please Note that the whole purpose of doing this step is to find the direction to which we have to slide our OF line and thus our selections are arbitrary.
Shokoufeh Mirzaei i love your voice.....
complementing a teacher for their voice isn't disrespect
hmm gud everything easily understandable thanks
Thanks you mam
Very good Explanation of the graphical method to solve LP problem
Tysm
Yes mam this is only to find exact optimal point. So as to reduce unnecessary work of finding another point. You are just par excellent mam.
Thank you so much Miss Shokoufeh! Your linear programming videos saved my life. Literally thank you so much, keep up the good work!
thank for making life easier ,some professors insisted to complicate things on purpose ,thanks again for you and the social media that connected you to the world .
Some people are just better teachers than others. You are proving quite useful to me already.
you explained it better then anyone else on TH-cam!!
I HAVE BEEN TRYING TO UNDERSTAND THIS FOR WEEKS THANK YOU!!!!
Best lectures covering Optimization, thanks a lot Shokoufeh.
Very Nice Explanation. Best explanation video that found on TH-cam so far. Thank you. Good Job, Keep Going.
Thank you this was helpful, but I do believe you can also find the maximum value by taking the points of the vertices of the feasible region and plugging them into the maximum value equation, and the greatest value from those is the maximum value.
Very good video, I figured it out 3 mins into your video.
This video helped me soon much thank you Mirzaei! I have a project due tomorrow and I ACTUALLY understand this!
+Judy Blanco Hey, could you maybe help me? I understand most of the video, but at the part where she calculates the optimal solution at the intersection of constraints 1 and 2 I lost it (at 9:49). Can you explain me how she got -x and -80? It will help a lot!
+Panic Flupbaster to solve the system of two equations, I multiplied the two sides of the second equation by (-1) and added with the first equation. this way, when you add the first and second equations you ll get rid of x2 and can solve the equation for x1. when you have the value of x1, you can replace it in any of the two equations and get the value of x2.
+Shokoufeh Mirzaei ooh i get it, thank you very much, this video helped alot! :)
I'm stuck on how to solve the system of the two equations as well - how did you pick (-1) as the figure to multiply the second equation by? The more I try to find different examples, it seems that this is an arbitrary figure? Thanks so much, Erin
Impressive and most helpful. I did this course years ago but need to brush up to solve my current problem.
I'll definitely look at the other videos, in a crash course format. -- Immense gratitude.
This was so much clearer than my professor thank you!!!
Literally i passed toughest exam of my masters by learning via your lectures. Thanks 😊
Lady you are a genius, you have a gift for teaching
this was awesome....it really seemed tricky by looking and listening...but practicing was the best thing to catch up with the content...
Best explanation of LPP !! Thank you so much !!
you are really a life saver . Thank you from my bottom of my heart
LIFE SAVER!!!!!!!! Thank you so much for such a crystal clear explanation.
EZ pass on my midterm exam! Thanks!
U r the saviour mam thanks!
Nice mam
Straight and clear, good work
Thanks a lot! It really took me 11mins to understand the concept. Great work!
Thank you for the video. Simple, clear, and detailed explanation of the concepts.
Am glad I found this explanation
Thank you for the simple explanation
Thanks a lot for your time and effort. This was very helpful.
nicely explained the problem, you are a good teacher
nice voice mam and way of teaching is also good.
Thanks...I totally understand it now... keep up the good work dear.
Your tutorial is so simple to understand. Thank you.
Which software do you use to record your tutorial?
Thanks! I used Doceri
Yes you explained it very well. You are the best
Great explanation and straight to the point. Thanks a lot
You teaching skills and knowledge is amazing mam..may Allah bless you. Loads of love ❤❤❤
Holy, I never thought it was this easy
Short & Sweet. Great video, Thanks a lot
Thank u so much been struggling graph the objective function. Now I totally get ohw n u made find the optimal solution way easier keep at it.
Thanks a lot. BTW, the line for the second constraint in the last question is a mistake, right? Cos the line is at X2 = 2 not 3.
It's a mistake, right?
you are delivered beyond enough, Thank you very much I have learned a lot keep as it is
straight forward and amazing
Thank you so much for the video. You made it very easy.
Thank you for this!!! I finally understand thanks to your video :)))
So clear and easy to follow! Thank you :)
Thank you, may God reward you well
Thank you so much, Shokoufeh!
thank u it was so helpful for me
It's a lifesaver. Thanks.
thanks a lot. it was really useful. if i had the whole question description that would be perfect. because i want to learn how to make objective function and constrains formulas.
Ahsant! kheili khub tozih dadi. well explained thanks
hey, how did you graph 3x+2x= 60, you have the first line cordinates equal to x1=20 and x2=40 shouldn't x2 be = to 30?
Exquisitely explained...moreover ur voice is pretty appealing...thanks..keep up d good work
Waouh amazing explaination. Thank you
Special Thanks for your effort.
Perfect explanation
but I have a question in the first case where is there a feasible solution, can I calculate the profit at the intersected points taking in consideration the feasible area so I will have only 2 points, then i try solving the equations of these two points and choosing the higher one instead of trying to draw the objective function many times ?
Yes, you can do that. Indeed, even though its not the formal way of finding the optimal solution, we suggest students doing it when their drawing its not properly scaled and they are not sure which point is exactly the last point that the objective function line hits as it exits the feasible region. But please note that you have 5 corner points (not three), which are (0,0), (40, 30), (40, 0), (20, 60), and (0,80). so you have to calculate the value of objective function for all the corner points and pick the one with max (min) value.
If you already know the direction of objective function but you are not sure between the points (40,30) and (20 ,60), you can only calculate the value of OF for these two points and pick the one that has a higher value.
Really Appreciate your work and answer thanks :)
useful for one night before exams... thanks mam👍
Plus point for a concise explanation. Thank You. Now, I have a question: why is the optimal solution found in the intersection points and not inside the feasible area? Any insight will be appreciated.
+Lirila Mzr There are some theorems about the graphical method resolution, one of them says that the optimal solution is one of vertices of the polyhedra created by the restrictions, usually when we have a max. problem we use the farthest vertice from origin, the opposite is valid for the min problem, this time we use the nearest vertice from origin.
+Lirila Mzr OBS: You have to consider the distance from origin using parallels from Z function drawn.
Excellent explanation. Thank you! :)
Thanks for sharing. Please also upload how to solve for problems with more than 2 decision variables-the simplex method
It is already posted. Please you go to my channel to see all the videos that are posted.
if x1 is nt given den how can we find d feasible solution
Thank You Miss.. It's really helpful..
Well explain, I hope I can do better in this topic of linear problem.
As you have said in that video that the line we're gonna draw for objective line should be equal to z. So the first line(obj. F) is 60, then you drawn a line that would be equal to z which is 60(40 +20).in that case, we're gonna forget the 20x1 and 30x2 because we should follow the rules right? So we would make the obj. F line equal to z(40 plus 20 = 60) because of your graph there. is that correct? And the second obj. F line, it should have equal to 120 (as you assumed) but you drawn a line with 40x1 and 60x2 that equal to 100, since the second obj. F line is not equal to z=120, can you explain to me what's going on there? Im just little bit confused there. And just asking here.. Thank you. :)
This was a great help! Thank you!
That was a neat presentation!
Very Useful... Thanks a lot!!
Thank you... It really helped me a a lot.. 👍👍
What happens when you make X2 to be on the X-axis and X1 to be on the Y-axis (When you interchange the X1 and X2 coordinates) Does this change the end result? How do you determine X1 and X2 are on which axes?
no, this will not change the final result and your objective function value at the end will be the same.
thanx ur awesome.....
also I hope u exeplaine forcasting & assignment & inventory. prop too and thanx agine
thanks a bunch, was very helpful............
Good day, can anyone assist. Why the portion where line 3 and 2 intersect not included as the feasible region? TIA
simply perfect and thank you!
You're the best
Thanks
I think you have drawn the line for 3X1 + 2X2 =60 wrong because it should intersect the number 30 in the X2 axis but you have intersected it on the number of 40.
+goksun v : shes done it correctly ,watch close, its between 20 and 40.
goksun is correct. she did not plot through 30 but 40. these lines should be parallel to line II if drawn correctly
Nice Explanation, but It would be better if you had showed the question or the problem into the video since it is confusion that what is the question, the beginners
The question is in the title "How to Solve a Linear Programming Problem Using the Graphical Method"
Hello! I am doing a research paper on these types of problems in my Calculus two class, do you know how to intertwine the two? Also wonderful job, I have never done any of these in my lover div. economics classes, but after this video I will be able to no problem as I get further.
+Hector Prado sorry for the late response, I can definitely help. send me a message to discuss this further if you are still intrested to know how to connect the two. smirzaei@cpp.edu
great explanation!
So good i am easILY able to understand it
What do we do with constraints that have equality constraints? and what about those which have non positive RHS?
Thank you
thank you, very clearly explained
What would be the minimum of the example in the video? (0|0) ?
Thanks. Good explanation.
hey thanks...plz can u help me for a solution of lp??
thanxx for ur video and voice....
its awesome and excellent sir
Maam please reply me
I could not understand that part z= 60 ..while the points are 30 and 20
Dr. Mirzaei
This is an amazing presentation!! Well Done!
May I ask what tools you used to create it? I'd like to create and present a series of videos similar to this one to teach linear programming to my classes, and I'd like to include animations for the objective function. However, your whiteboard and blackboard visuals are quite good, and would make an excellent start for my classes. Thanks in advance.
Hi Rodney, Thanks for your feedback! I am using Doceri. It is an ipad app and you can make animations with it! Let me know if you have any questions.
Thanks, that was very helpful.
You saved me thank you so much
why did u graph the numbers wrong for the Z value it should be (0,40) & (60,0) but u switched them?
THank you for your explaination, however I am confused as why you subtracted constraint II from constraint I at the end when finding the optimal value for xsub2. I tried (out of curiousity) subtracting I from II and got -x ≤ -20, which (after dividing by -1) gave me x ≥ 20, which is not the same. Should I be using an equals sign there since the direction is no longer relevant when finding the optimum points? Thanks!
The intersection point of the two constraints falls on both lines, that's why we have to find the intersection point by solving the system of equations formed by the two constraints crossing the point with equal signs (because the point is exactly on the lines, not on one side of the lines). What I did there, helped me to solve the system of equations with two decision variables and two equations. You should know how to this from linear algebra.
amazing tutorial thanks
What about when they ask for minimize z? Is the constrain going to be greater just like the video or is it going to be less than ?
handling of min problems is explained in the video. Please watch it again without skipping. for constraint with >= you exactly do the same procedure. There is no difference in the steps you implement. Just that you might end up choosing a different side of the line as your feasible region. you will figure that out by plugging a chosen point in the constraint, as explained in the video.
Great video!
very helpful thank u
i am not understanding how get 3x1+2x2=60
When you are finding the optimal solution, using the lines I and II, why does the second line become negative (-) while the first line is positive? 2(x1)+X2 = 100, but x1 + x2 = 80 because x(-1) x1+x2=-80 ...thank you.
I multiply the second equation by (-1) so that I can cancel out X2 when I add the two equations.This way I can solve the resulting equation for X1. Then, I replace the value of x1, that I have found, in one of the equations (in this case equation 2) to find the value of x2.
Thank you so much. Great video. Has been a lot of help.
Hello! I got 2 constrains ,0.03 X1 - 0.01 X2 ≥ 0 and 0.21 X1 - 0.3 X2 ≤ 0 which both give (o,o )! . How can we draw them correctly? Thank you a lot :)
thanks for the great explanation
How we assume 60,120 by self? didn't get