in-the-following-exercises-solve-the-given-maximum-and-minimum-problems-the-rectangular-animal-displ

Question

In the following exercises, solve the given maximum and minimum problems.
The rectangular animal display area in a zoo is enclosed by chainlink fencing and divided into two areas by internal fencing parallel to one of the sides. What dimensions will give the maximum area for the display if a total of $240 \mathrm{m}$ of fencing are used?

Linh Vu · Accepted Answer

Dr Judy Nother Dimension under Terra Ridge in here as x and y on, we want to define this reaching him to the DuPont. So buying, but allow ah fans here and doesn&#x27;t record is another. Why? He also had three wives and two ex. And now we have only 400. Fit of fencing is used. It means that the perimeter it got your 400 you go, Joe three. Why? Because we have one Jew and three wise. Let&#x27;s do acts on Lee, so have to act. So from here, we can see that. Nah, why? We could do for 100 months to act the writing by three. And from here we haven&#x27;t under area as a former X Times Kwai. And because we have why could you just once so I can put it in. And then we have X times for 100 Minister, actually, remember, tree I can be written that is a minister X square on the tree and now bless for 100. Uh, on Victory X on now, the maximum area, we&#x27;re going to send it about attacks and the vortex are girls and the value of X equals humanists being with you I Don&#x27;t Go. Joe minus 400 number three. The Wedding by Jud Hamm&#x27;s Once to Amber Tree To get a good Jew minus 400 on between, we multiply by the reciprocal on the second fractions, so we&#x27;ll be three on top and it&#x27;s far tree concerned with a 3 400 The manners with the manners 400 leave, every four will be 100. So actually get your 100. Then why would you go Jew for hundreds minus Julie times 100 running by three to echo Jew 100 Andi running by three and a maximum area where you go Jew No, 100 times 100 I&#x27;m a tree So you go Joe Won t phone divided three.

Ma. Theresa Alin · Answer

consider the figure below that illustrates this problem and here we let actually go through with and why go to the length now in optimization problems. The first thing you have to do is to determine our objective function and this problem, the objective function is the one that&#x27;s being maximized and so It will be the area 80 which is equal to product of the length and width, that&#x27;s X times Y. Next you want to write our objective function in terms of one variable only, how to do this. We use the fact that the total fencing used At 600 ft. Then this means that 600, this is equal to we have three y plus two x. Now solving for Y. In terms of X, we have Why? This is equal to 600 -2 x. All over three. Or that&#x27;s a shame as 200 -2/3 x. Since X and Y are dimensions then they&#x27;re both greater than or equal to zero. And if X and why are greater than or equal to zero, then 200 -2/3 x. This is greater than or equal to zero and this tells us that zero is less or equal to X. So less than or equal to 300. And so our objective function would be a this is equal to X. Y. Or that&#x27;s just x times 200 minus two thirds X. In which X is in between zero and 300. And simplifying this, we have a that&#x27;s equal to 200 x 2/3 x squared. And then from here we would find the derivative of e to get the critical points. And so by power rule we have a prime, that&#x27;s equal to 200 minus. We have two thirds times two X. Or that&#x27;s just 200 -4/3 X. Next we want to set a prime 20 and solve for X and so we have 200 minus four thirds X. This is equal to zero and we get X equal to 150. Now, since X is in between zero and 300 and we have the critical .150 than to find the maximum. We have to use the concept of absolute extreme. Er that means we evaluate a Using the endpoints zero and 300 and the critical point X equals 1 50. That means we have A of zero, this is just zero times 200 -2/3 of zero And this is equal to zero. Next we have a of 300, this is just 300 times 200 -2 3 of 300 And this is also zero. and then lastly we have a of 150, this is 1 50 times 200 -2/3 of 150. This is equal to 15,000. And so the maximum area would be 15,000 ft and the dimensions would be X equal to 1 50 and we have why? Which is equal to 200 -2/3 of 150 And this is just 100 ft.

Debra Garey · Answer

okay, We are doing rectangular area of land with a fence, and we&#x27;re gonna have its section into two sections with fence going parallel to the two sides. So we know that we have 1200 feet offense, and I&#x27;m gonna make this side axe and I&#x27;m gonna make this side axe and I&#x27;m gonna make this side axe. So I&#x27;ve used up three ex feet offense. So for I&#x27;ve had 1200 feet to begin with, I used up three ex feet and I have that much. That expression describes what I have left, but I have two sides I still need defense in, so I&#x27;m gonna divide that by two. And that&#x27;s the meat of my dimension for this side here. Now I want to maximize area. So to write the equation for area I&#x27;m gonna do my length times with. So I&#x27;m gonna have X Times 1200 minus three acts, all divided by two. It&#x27;s gonna be area of my fence, which we want to maximize. So before I do anything, I&#x27;m gonna simplify this expression which would give me 1200 x minus three X squared, divided by two. And I&#x27;m gonna take it one step further and make it 600 X minus three halves X squared equals my area. Now, to find my max from area, I&#x27;m really interested in the Vertex. So I&#x27;m gonna flip this around in tow. What would be standard form? Okay, so for my Vertex form, I&#x27;m going to use that same old formula X equals the opposite of be over two A. So I&#x27;m gonna say X equals the opposite B is negative. 600 divided by two times a, which in this case, is negative. Three halves, Which gives me negative 600 divided by negative three. And that gives me an X value of 200. So if this is 200 and this is 200 and this is 200 I&#x27;ve used up 600 feet. Offense. That means I have 600 left. And that would give me 300 down here and 300 up here. I could also take 200 substituted into here and get the same answer. So, in the final part of our problem to actually answer the question, we&#x27;ve done a lot of math. You gotta make sure you go back and answer the question we have a field that is 200 feet by 300 feet, so our maximum area is gonna be 60,000 feet. Always make sure you&#x27;re answering the question when you do these.

Ankit Gupta · Answer

owner has 80 feet offense to in close a rectangular garden. One dimensions for the garden give the maximum 80. So let&#x27;s take X is equal to one side, and why is equal to the other side in the pedometer is given us okay, Twix, but a stool by is equal to 80. Why is equal to 80 minus two bricks by two? That a sequel toe 40 minus six area off district angle is X in Dubai with his equal do X in tow. 40 minus six that is equal to minus X squared. Bless 40. So the function y is equal to three off X is a quadratic negative leading Don&#x27;t. It&#x27;s graph is a parable of opening down, and it has maximum in its vortex. So be deter. Mined the coordinates as X we comma by movie XB will be minus B. By doing that is equal to minus or 40. By doing two minus one, it is equal to 20 and vie V will be a or 40 he off 20 so that will be equal to 20 square plus 40 into 20. So that is equally do 400 hints divide. Would it be 40 minus six B, which is equal toe 40 minus 20. That is equal to 20 so hint they size of the rectangle is 20 feet. Coma, 20 Fink.

Linh Vu · Answer

so consider an ah tango, Uh, reach in here and we find the dimension is angst And the why here. And because we have, ah, 80 years, a fencing so means down the perimeter. It could you I d on. We should have a go to gently at you express to you. Why? And from here we can actually the wind it was gonna go with Joe, I deem honest. You actually remembered you and it could you from the minus X What? The minus ANC&#x27;s. And now the area price on the dimension here was gonna coach your ex im skwy. And now, because one gorgeous gone today so we can go have to replace it for the minus X and good Germans next grab less for the X. We want to Mexico Mayes the area. You shouldn&#x27;t go inside, you know. But next on, we know the vertex occurs and a very X equal. Germany&#x27;s Bayer, which you I so could you minus 20 dividing by zero times minus once a record. You must 40. You&#x27;re running by ministers. I could you 20 When Mexico Genting Why we go to for the ministry, aunty. So it could you don&#x27;t they? So it means that we have here. We were in the square gently and trendy and now the maximum area to decode your 20 times 20 Got your 400.

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In the following exercises, solve the given maxim…

Problem 18 Easy Difficulty

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Anna Marie V.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Catherine R.

Anna Marie V.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus