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A barnyard is to be fenced is as indicated in Figure $22 .$ If 6000 feet of fencing is to be used in its construction determine the dimension $x$ and $y$ that will maximize its total area?

$$x=375 \mathrm{ft}, y=500 \mathrm{ft}$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Oregon State University

Baylor University

University of Michigan - Ann Arbor

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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A barnyard is to be fenced…

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A rancher has 1000 feet of…

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A rancher has 200 feet of …

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You have 1000 feet of fenc…

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A rancher has $3000 \mathr…

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One thousand feet of chain…

for the given problem, we're looking at fencing, You know that 6000 ft of fencing need to be used in construction. Um and we want to maximize the area, so we know that the area is going to equal X times Y. Um So let's just have that be um Our area is the base times the height, and then we also know that two X Plus two Y. Since this is a rectangular fence, um we know that that's going to be Equal to 6000 ft in total. And then we can essentially set this equal to um we can set this equal to X or Y. We know that we want to maximize the total area of them. So the way that we can do this is by relating um X to Y. And plugging it in. So if we move this over, we see that X is going to be 3000 minus Y. So we'll plug that into the area of maximizing, we'll get the X is 375 ft and y is 500 ft

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