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In the following exercises, solve the given maximum and minimum problems.The sum of the length $l$ and width $w$ of a rectangular table top is to be $240 \mathrm{cm} .$ Determine $l$ and $w$ if the area of the table top is to be a maximum.

03:28

Carson M.

09:27

Wen Z.

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 7

Applied Maximum and Minimum Problems

Derivatives

Missouri State University

Campbell University

Baylor University

University of Nottingham

Lectures

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who? So the surface area for this question? All right. It's gonna be uh so you know that it has a six surfaces, right? That cuba six surfaces to identical South africa. This is gonna be two X. Y. Two N. C. And two Z. And that's gonna be the total surface area which is uh 1500. So if you divide through by two that's gonna you're gonna get this okay? Of course. For the length we got four of the X. Four of the Y. And four of the Z. That's gonna be 200. And if you divide through by four you're gonna get that. Okay? So from this expression here have Z being go to 15 50? Uh my sex one is Y. Right? So in uh X. Y. Z. Here we are substituting for Z. Okay? And that's gonna give you this. Okay? So you need to set a constraint. So we have Xy. Right. Plus Y. Z. So we are using this you're saying this? All right. So you got X. Y. You got Y. Z. But remember Z this right here, Right. So you are a presidency we are eliminating. See okay? So whatever you see, see you put in the expression so Z goes here, of course. He goes there. That we go to 750, okay? That we just uh responded bracket, you know, and the certification is going to lead to die. Okay? Then we're gonna use the divergence. Okay? And that's going to lead to that. So from here, almost that's just algebra. Okay? And we're gonna get our maximum to be done and then our minimum two down. Okay? Thank you very much.

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