Hello everyone, this is Mirzaei from Cal poly

Pomona and in this this lesson we are going to learn how to solve a linear programming

problem using the graphical method We usually use the graphical method for problems

with two decision variables The reason that we do not use the graphical

method for problems with more than two decision variables is the complexity of their visual

representation Now for problems with more than two decision

variables we later introduce the Simplex method Now let’s look at one example to see how

the graphical method works. Suppose we have a maximization problem subject

to a set of constraints Now to solve this problem graphically we need

to implement two steps The first step is to draw the constraints,

and the second step is to draw the objective function

In an optimization problem, when we draw the constraints of the problem, we form an area

which is called feasible area or feasible region

The ultimate goal for an optimization problem is to find the best value of objective function

within that feasible area Now if you look at the constraints that are

given in this problem, you see that they are all in forms of inequality

The area that is given in by an inequality usually includes the line that forms the inequality

and the points in one side of that inequality Now, to deal with this condition and find the

feasible area given by an inequality we first assume that each inequality is in fact an

equation which represents a line Now To draw a line in a two dimensional space

we need two points We usually find these two points by once setting

X1 equal to zero and once setting X2 equal to zero.

For this line, if I put X1 equal to zero then X2 will be equal to 100, and if I put X2=0

then X1 will be equal to 50 Now having these two points I am able to draw

a line represented by these two points Ok, if I find the two points and then connect

the two points that are given here, I am able to draw this line.

Now, to check what side of this line I am looking at in this inequality,

One way is to pick an arbitrary point which is not on the line, and see if satisfies the

inequality or not, If it does we are looking at the side that

includes the point Otherwise we are looking at the opposite side

By standard we usually select the point (0,0) if it’s not on the line

and in this example if I select point (0,0) which is the center of the coordinates here

Now if I put this point in the first constraint and replace X1 and X2 by zero, you see that

zero is less than 100 so the constraint is satisfied

So, we are looking at the side that includes the point (0,0).

We can show this conclusion with an arrow on the line.

Now if I draw the second line of this problem, again by setting X1 and X2 equal to zero,

I am able to find two points Where if I connect these two points I can

get the second constraint line Now To decide what side of this line we are

looking at in this inequality Again we replace the point (0,0) in the second

constraint and check whether the condition is satisfied

or not By replacing (0,0) the condition is true

So we are looking at the side that includes (0,0)

Remember to name your constrain as you move forward

Because later on we might be interested in finding the intersection of lines

and it will make your life easier to know what lines you are looking at or what is line

equation that you need to pick to find the intersection point

Now the last constraint is X1=3 this line represent the second constraint

and we are looking at the side that doesn�t include (0,0)

because zero doesn�t satisfy this constraint. Now To form the feasible area of the problem

I need to find the intersection of these two areas.

Since both X1 and X2 are positive, we are in the first quarter of the system

of coordinates and there is no intersection for these two

areas in this quarter. Therefore, there is no feasible area.

So the LP does not have a feasible answer

thanks a bunch, was very helpful…………

Straight and clear, good work

Best explanation of LPP !! Thank you so much !!

Can anyone help me to formulate this problem,,In my understanding there will be 2 variables in the objective function but what will be the constraints???

"""""""""Because of the arrival of new models ,a salesman wants to sell off quickly its stock composed of 8 phones,4 handsfree kits and 19 sim cards.He can propose an offer with a phone and two sim cards and that will give him profit of 7 dollars.Similarlay,he can prepare a box of 1 phone,1 handsfree kit and 3 sim cards,yielding a profit of 9 dollars.He is assured to be able to sell any quantity of these two offers within the availability of its stock.What quantity of each offer should the salesman prepare to maximize its net profit?""""""

Thank you so much for your hands and voice

you are really a life saver . Thank you from my bottom of my heart

wow

HI !!

I dont love your voicebut i love you alot…..

Спасибо за видео

Спасибо за видео

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 🙂

+Shokoufeh Mirzaei thank you for the explanation. can you make an example about minimization problem & graphical method solving ? i m stucked in a problem i can't solve :/ .

What do we do with constraints that have equality constraints? and what about those which have non positive RHS?

Thank you

This video helped me soon much thank you Mirzaei! I have a project due tomorrow and I ACTUALLY understand this!

الي جا من قروب الشقردية لايك

hey thanks…plz can u help me for a solution of lp??

I love you.

nice voice mam and way of teaching is also good.

Bullshit! You don't really need objection functions. Just looks at the terminal points-the (0;80); between 1st and 2nd lane; between 1st and 3rd lane; the (40;0) and the (0;0). Substitude the equation with the values in each of the points and see in which of them the equation reaches it's maximum. You don't even need to calculate all of them. It is obvious that the maximum is either in the point between the 1st and 2nd line or the point between 1st and 3rd line and you have to chech only those two points and figure out which gives a maximum for the given equation.

very clear

Thank you so much, Shokoufeh!

(80,0)

~~—~~> gives us z=240 ,and (20,60)~~—~~> gives us z=180?so optimal solution should be at point (80,0) no?

i am getting confused :/

THANK YOU!!

For finding direction we will always take (0,0) to identify whether they are greater or less than constrain value? anyone explain plz. i m a little bit confuse. #Shokoufeh Mirzaei

This was a great help! Thank you!

Lady you are a genius, you have a gift for teaching

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?

your handwriting is not good

thank u it was so helpful for me

Can you solve the optimal problem without using the graphical method?

thank youuuu 🙂

Thank you so much!

Thank you… It really helped me a a lot.. 👍👍

useful for one night before exams… thanks mam👍

mam. every explanation was awesome…bt plz improve ur handwriting😂

Thank You Miss.. It's really helpful..

what if the constrains have something like <=-4 ..

should we change this constrain by multiplying the constrain by -1

how did you solve the 2 lines of the intersections?

your voice is amazing i love it ?

she sounds like a small kid

thanks

Thank you

what to do when the feasible region extends till infinity … i mean please explain for other cases too.. i mean for the problems occuring when we have found the feasible region

Mam your accent are fab

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.

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.

Good one 😇

I posted a graph of the feasible region,

https://www.desmos.com/calculator/akserfw40w

You can move the slider to see the objective function line move

great job

its awesome and excellent sir

Thanks sir

fantastic video

but i also recommend you about TIB Academy in Bangalore

they are also best in many other course.

https://goo.gl/TSDVBH

thanxx for ur video and voice….

you should improve your writing skill

Thanks

Hello; can you solve my problem by simplex lineary program please ……..x+y=6; 3x-2y>=3 and x<=5 if 《x & y》>=0

explanation 👍👍👍

Ahsant! kheili khub tozih dadi. well explained thanks

Thanks, You are saving my ass 😛 Very good explanation.

Thank you so much!

amazing tutorial thanks

Thanks. Good explanation.

That was a neat presentation!

I didn't get how did you find the feasible area?

Awesome!

U r the saviour mam thanks!

it is best way

How to solve linear programming problem by graphical mathod :

Maximize π=40×1+30×2

Subject to

x1≤16

x2≤8

X1+x2≤24

X1,x2≥0

Mam how to solve this problem graphically max .3×1 + .9×2

S.t x1 + x2 greater than equal to 800 ; 0.21×1 – 0.30×2 less than equal to 0 ; 0.03×1 – 0.01×2 greater than equal to 0

thank you , how to shade the region

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!

Thank you, may God reward you well

Very Useful… Thanks a lot!!

Does I assumed any value for Z??or there’s conditions?

EZ pass on my midterm exam! Thanks!

You have amazing voice😍

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 ?

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.

Niceeee

Thank you

Bakwas

Thank you

great video

thanks that was helpful

LIFE SAVER!!!!!!!! Thank you so much for such a crystal clear explanation.

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

Would it not have made more sense to use A and B as opposed to X1 and X2? this way when you multiply something in the formula it doesn't look like X1xX2xxXxX!x1x12x12x2x1x2x1x2xx1xxx2x1xx2x12 ? :/

helpful indeed

i am not understanding how get 3×1+2×2=60

So good i am easILY able to understand it

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

Clear explanation

tnx

Nyc

Plzz your mobile no

Your tutorial is so simple to understand. Thank you.

Which software do you use to record your tutorial?

amazing

nice one

I HAVE BEEN TRYING TO UNDERSTAND THIS FOR WEEKS THANK YOU!!!!

you are delivered beyond enough, Thank you very much I have learned a lot keep as it is

Fatemeh it's amazing:)