Optimization Problem #4 - Max Area Enclosed by Rectangular Fence
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- Опубликовано: 3 май 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)
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
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
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
Calc final on Thursday. You and your vids just might help preserve my grade. Thanks Patrick!!
Dude your videos really helps me, and are crystal clear, thanks a bunch !
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
It's amazing to think people came up with these formulas. Thanks for the video.
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...
Your amazing! These videos are so clear and its so easy to follow your thought process to picking apart a problem. Thank You!!!
you are very welcome!
I did this by myself after watching you do problems # 1 and 2. I LOVE YOU!
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.
Thank you so much! You really broke down the process and concept of optimization. Everything made so much more sense!
Thank you for posting these videos!!! They are a real help!!!
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....
thank you so much for all of your videos!!
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.
very conceptual videos thanks patrick
I got this exact problem on my online exam but with 800ft lmao good looks bro thanks for the help 😂
Ah, thank you SO much! Perfect detail and clean handwriting unlike my 70 year old retiring college professor! Thank you thank you thank you!
Very smart guy. I have never seen such a great Math teacher. May God Bless you. Thank you thank you so much.
Thank you very much! This was extremely helpful
I am still very thankful for all your videos as well as Khan academys videos ... you guys are the best 1000000000000000 THANKS
Honestly, this is helping me so much! Thanks a lot!!!!!!!!!!!!!!
you are a lifesaver....best teacher ever!
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!
that's so clear video to learn how to solve...Thanks man !
patrick!! u da man UR AWSEOME- love from austria !!!
Once again reliable source for homework!!! Thanks for the vid!!
I LOVE YOU! thank you so much for this video!!
I appreciate this so much! Thank you!!!!!
Thank you. This helps so much
this was really helpful, thank you
Best explanation I have seen anywhere.
Many thanks just what I needed
Very helpful. Thank you!
Wow dude thank this helped a lot, I was completely lost but I now know how to do it
These videos are amazing!
You saved my skin buddy. Thank you for the videos.
Thank youu soo much very clear and easy to understand
This is so helpful thanks so much!
I did it on my own and then saw it was correct ...wwwEeeee!! Thanks Patti
Thank you patrick!!
You're better than my calculus teacher! And my calculus teacher is pretty great...
oh what an amazing teacher you are !! thanks alot
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
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
@darkwolf811 yep
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".
i just want to thank u from my heart!!! You legit saved my ass
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.
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.
patrick i wish you were my lecturer man you making maths so simple :)
@djerock72192 no, i will be using it
Wish me luck on my Exam tomorrow and thanks for the help!
THANK YOU SO MUCH
Thanks for helping me for my exams
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.
I was not aware of the part where you substitute x-values to see if the dimensions increase/decrease. Thank you once again!
very-very nice video ! thanks man :)
thank you my guy
thanks man this helped a lot
No problem!
Thank you!
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!!!...
u have no idea how many lives u saved by posting up these videos :P thanks =)
Dear professor, may l ask you a question, is optimization an exception or a part or infinitésimal calculus ? Thanks.
Good. Thanks 👍
@nanone1994 congrats on your great score :)
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?
This legitimately made more sense than how my teacher taught me...
...who spent 3 days trying to explain this
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 :)
Thank you Sir..
Thank you
Thanks man
@chewedtoothpicks It's only 3 sides not 4, 2 widths and 1 length or vica versa. The river is the 4th side.
can we use the second derivative test to test if it's a max or min instead of doing the interval test?
you're my hero.
just got a homework question right, Thanks!
You're the best ,, thanks man
THANK YOU
I had this EXACT problem on my Calc 1 quiz last week.
you are a lifesaver
Extraordinary
@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
thank you
You are intelligent, thanks
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?
You are my calculus angel!
Happy birthday girl
Fucky..😘😘
Thanks!
GAAAHHHHH YOU MAKE SO MUCH SENSE!!!!!!!
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?
I have a question, if the river fence is included, will the length become (250-2x)?
Ha ha! Our teacher used this problem as an example in class! That means a problem like this will probably be on the test...
Can you also find out the two values by completing the square?
MARAMING SALAMAT!
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?
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 .
Hopefully someone answers but how would you put the area function into a graph?
what do u do when ur given the max area and have to find the dimensions that minimize perimeter????