Це відео не доступне.
Перепрошуємо.
Optimization Problem #4 - Max Area Enclosed by Rectangular Fence
Вставка
- Опубліковано 3 тра 2011
- Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) / patrickjmt !! Optimization Problem #4 - Maximizing the Area of Rectangular Fence Using Calculus / Derivatives. In this video, I show how a farmer can find the maximum area of a rectangular pen that he can construct given 500 feet of fencing. We can actually solve this quite easily using algebra but here I am trying to show the overall process that we use on maximization / minimization problems.
![How to Solve ANY Optimization Problem [Calc 1]](http://i.ytimg.com/vi/cUMvwG7wvzM/mqdefault.jpg)
that moment when a 10 min video made more sense than a 2 hour class teaching about the same thing...
*****
I know, might as well not even go to class.
Yup, got my final tomorrow.
@@11beddiev36 LOL ZD
Exactly
Thanks dude. I'm going to do that with my cows.
I think Donald Trump will do a calculation similar to this one to build his wall
Ellie Burggraff that’s assuming he can even elementary math
@@GetUpAndWatchVideos That's assuming you can even speak elementary level english
@@jonathanwebb6524 'assuming "
GetUpAndWatchVideos ok
My typical after school schedule: 1st period Chemistry with Tyler Dewitt and 2nd period Calc with patrickJMT
ha, that is a good schedule! :)
would be nice if Tyler covers some orgo and physical chems
Too real
5 years later, comment is still relevant 🙃
gotta love cramming before finals....
me right now for my calc 1 final
@@fuccckckkkkckkck same here, the only topic I absolutely do not know how to do... and worth about 9-11 marks..
5 years later and still relevant
Manny bump.
It is my first one tomorrow in the morning XD
It's amazing to think people came up with these formulas. Thanks for the video.
My guy, a girl sent me a problem like this and asked for my help. I haven’t done math since like 4th grade and I understood this perfectly. Thank u my guy
Calc final on Thursday. You and your vids just might help preserve my grade. Thanks Patrick!!
When I was in calculus I spent 10 weeks (the length of the quarter) trying to get this down.... and my professor barely helped me at all. You just made it ridiculously clear in under 10 min.
I labeled my rectangle differently. The side parallel to the river I labeled x and the other two sides I labeled y. So my equation was x + 2y = 500 and thus y = (500 - x)/2. Then A = x [ (500 - x)/2 ] which gives A = 250x - 1/2 * x^2 and the derivative is dA/dx= 250 - x. When I set that equal to 0, I get x = 250. Then I plug that back in my original formula and I receive 125 for my y value. A = x * y = (125)(250) = 31,250 square feet. So my computation was different but I still received the same answer!!!
The way you did it was correct for a 4 sided pen. However, the question said that the pen has 3 sides, the 4th side is the river
@@Amanda-bg7ibHe did it correct. He set the problem up for a three sided pen, hence he used the equation x + 2y = 500. He used different variables, but the naming of the variables mean next to nothing, as you are free to refer to them as you want. If he set it up for a four sided pen, he would have used the equation 2x + 2y = 500.
This was a fantastic video. I've been stuck on this kind of problem for 45 minutes now. Your video has really cleared things up for me. Thank you!
You should have used differentiation dude...
Will do man..there's many foreign students here who do not understand a thing the lecturers are babbling about in class, cause everything's in Chinese...your videos are life savers for some of us...cheers....
I got this exact problem on my online exam but with 800ft lmao good looks bro thanks for the help 😂
Dude your videos really helps me, and are crystal clear, thanks a bunch !
I did this by myself after watching you do problems # 1 and 2. I LOVE YOU!
patrick!! u da man UR AWSEOME- love from austria !!!
Very smart guy. I have never seen such a great Math teacher. May God Bless you. Thank you thank you so much.
Isn't the length 500-2x divided by 2? 500-2x would be the two lengths together and not just one.
Yeah, Even I thought that is should have been x(250-x)=Area. The answers are same here, may be due to differentiating and equating to zero. I think answers would have been some what different otherwise.
in this case, u can just divide the fencing material to 2 then that will be your length. the remaining fencing material will be divided by 2 then that will be your width. now that you have your length and width, multiply it then that'll be the maximum area.
Ah, thank you SO much! Perfect detail and clean handwriting unlike my 70 year old retiring college professor! Thank you thank you thank you!
I ended up doing it by constraining the perimeter. I said well if we only have 500ft of material to work with. The the perimeter is 2x+y. So, 500 = 2x+y.
From there I got y=250-x and I plugged that into the area, a=x(250-x).
I was scared I got it wrong when I saw you did it a different way but I also arrived at x=125.
Thank you so much! You really broke down the process and concept of optimization. Everything made so much more sense!
i just want to thank u from my heart!!! You legit saved my ass
I am still very thankful for all your videos as well as Khan academys videos ... you guys are the best 1000000000000000 THANKS
Best explanation I have seen anywhere.
You're better than my calculus teacher! And my calculus teacher is pretty great...
you are a lifesaver....best teacher ever!
@CaNaDiiAnBaCoN sorry, i only had 990+ videos up for you last week.
Gotta love it when all the math instructors that post on youtube use the same video editing software and place all the sound onto the subwoofer channel. Yes, it's just you guys, it's rare I find a video about Chemistry or anything else where they blended all the audio together into the subwoofer channel. Find a computer with more than a stereo configuration (someone actually using a different connection for the subwoofer to the back of their computer,) and see how it sounds for yourself trying to hear a voice on a subwoofer. How can you be that good with math but that poor using a computer?
You sir are amazing to say the least. You make me feel stupid because you make so simple it's like "wait how come I didn't think of that".
wish you were my math teacher..man I would pay to attend your classes..its a pity I am in China...your videos are so simple to understand..thanks for the free videos man...peace!!!...
you are very welcome!
Thanks for helping me for my exams
The real question here is why the farmer doesn't care about stream health? The pen should be a certain distance away from the streams riparian buffer or else the cows will be introducing crazy nitrates into the stream. You got to see the bigger picture here "farmer".
Ha ha! Our teacher used this problem as an example in class! That means a problem like this will probably be on the test...
Thank you for posting these videos!!! They are a real help!!!
Your amazing! These videos are so clear and its so easy to follow your thought process to picking apart a problem. Thank You!!!
Once again reliable source for homework!!! Thanks for the vid!!
Wow dude thank this helped a lot, I was completely lost but I now know how to do it
oh what an amazing teacher you are !! thanks alot
Honestly, this is helping me so much! Thanks a lot!!!!!!!!!!!!!!
@AceAites He was just pointing out that when you do this problem when it is not dealing with a rectangle or some area, that usually you find where A(x) is undefined. But he didn't because we don't have an undefined area!! :D
This legitimately made more sense than how my teacher taught me...
...who spent 3 days trying to explain this
that's so clear video to learn how to solve...Thanks man !
Thanks again, Patrick! I got the same number I had earlier, but I did it again following your video just in case (I had different numbers) so that I would feel better. Sometimes it's not about not knowing, but it's about doubting yourself. I am happy you helped instill confidence in myself; that is, that I actually knew what I was doing. XD
So again, thank you! :-)
+Magicus1 very happy i could help!
thank you so much for all of your videos!!
Many thanks just what I needed
very conceptual videos thanks patrick
I did it on my own and then saw it was correct ...wwwEeeee!! Thanks Patti
You are my calculus angel!
Happy birthday girl
Fucky..😘😘
I was not aware of the part where you substitute x-values to see if the dimensions increase/decrease. Thank you once again!
@darkwolf811 yep
Thank you so much. Optimization is the only thing I don't get in Curve sketching everything else is softtt cause of your helpful videos :D
You saved my skin buddy. Thank you for the videos.
@chewedtoothpicks It's only 3 sides not 4, 2 widths and 1 length or vica versa. The river is the 4th side.
I'm stumped with this problem:
You plant a rectangular rose garden along the side of your garage. You enclose 3 sides of the garden with 40 feet of fencing. The total area of the garden is 100 square feet. Find the possible dimensions of the garden. Round to the nearest tenth.
I don't get how to solve it.
Wish me luck on my Exam tomorrow and thanks for the help!
These videos are amazing!
u have no idea how many lives u saved by posting up these videos :P thanks =)
Does a rectangle always provide the most area? Or could you get more area out of a different shape but still 500 feet of fence. How would you figure out which shape could generate the most area?
patrick i wish you were my lecturer man you making maths so simple :)
I had this EXACT problem on my Calc 1 quiz last week.
GAAAHHHHH YOU MAKE SO MUCH SENSE!!!!!!!
This is an old video so I am not sure you still read the comments, but if I were to take the second derivative of the area, which would be -4. This indicates concave down, so A' '(125)=-4 is the local maximum? Since logically it would be increasing on the left side of 125 and decreasing to the right of 125. Also as an alternative way of finding the maximum could we instead find the absolute max on the closed interval [0,250] and the critical point 125?
you are a lifesaver
Thank you very much! This was extremely helpful
I LOVE YOU! thank you so much for this video!!
Thank youu soo much very clear and easy to understand
Extraordinary
Hopefully someone answers but how would you put the area function into a graph?
If you see the smiles of my friend and myself after this video. It means that we actually know how to do this now. We're jubilant
haha I thought his cows would swim away too haha until I read that
@djerock72192 no, i will be using it
Thank you. This helps so much
I love that people have to time and heart to make these videos. This is why I go to church.
Very helpful. Thank you!
well, i am always here at least :) spread the word in china for me!
Can you solve this quest:-
PQRST is a pentagon whose perimeter is p cm . PQT is an equilateral triangle and QRST is a rectangle if PQ is x cm find the ratio of p to x for which the area of the pentagon is maximum
I would personally like to see a video on optimization of rectangles or any other shapes within another
ex: a rectangle within a circle given the radius of the circle
thanks man this helped a lot
No problem!
you're my hero.
this was on my test and is the only video i did not watch about optimizations -_-'
Through problems involving the area of rectangles, Ive always found that the area is maximized when the rectangle is a square. Im just wondering why this isn't the case here. I understand the math behind it, but I don't get why it is any different here.
It's because only problems where you have 4 sides to worry about usually turn out to be a square. These kind of 3 sided problems usually turn out to be y=2x.
I've seen in other optimization video they would have constraint equation then plug it back into the area formula and then take the derivative of the area to find the critical value, but i don't see it here?
This kind of problem is the most common one found on tests.
just got a homework question right, Thanks!
We have this type of problem on our tests, but I'm in precalc so I don't know what a derivative is. I can't find any precalc videos for this type of problem. Is there a way to do these without the derivative?
Thank you patrick!!
thank you my guy
How is some random guy on the internet better at teaching then my actual math teacher?
you can just take the second derivative after you get the critical number and see if it is negative it means the critical number is the absolute max and if it is positive the critical number is the absolute min
You are intelligent, thanks
Took the BC Calc AP test today. Wasn't too bad. Though there was a Taylor series problem that I knew how to do the first half, but I would REALLY like you to explain how to do the 2nd half. Too bad I have to "wait 48 hours" before I can discuss the nature of the problem :)
Okay so If they do ask for dimensions is their like an extra step to do so because I have this problem (except it used 200 ft. And has two adjacent rectangles) but I don't know how to find the maximum area of dimensions .
@PhillipBroussard
Took me like 2 minutes and it's the first one I've done. He's teaching so he goes way slower than necessary for clarity.
this was really helpful, thank you
I appreciate this so much! Thank you!!!!!
After you’ve found the function to represent the area of the rectangle, being that the function is a downward opening parabola, wouldn’t the maximum x-value simply be the x-value of the vertex ( in which case we could use the equation x=-b/2a which is -1000/-4, or 125) ?
Yes
This is so helpful thanks so much!
when would you have to check if the equation is undefined?
or you can take the second derivative to ensure your x value is a max and in this case it is since the second derivative is -4 ( a negetive number?