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In the following exercises, solve the given maximum and minimum problems.U.S. Postal Service regulations require that the length plus the girth (distance around) of a package not exceed 108 in. What are the dimensions of the largest (volume) rectangular box with square ends that can be mailed?

Calculus 1 / AB

Chapter 24

Applications of the Derivative

Section 7

Applied Maximum and Minimum Problems

Derivatives

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:47

The U.S. Postal Service re…

04:42

03:50

Maximum Volume A rectangul…

06:06

Postal Regulations The U.S…

05:18

08:02

The sum of the length and …

08:43

A shipping company handle…

01:54

Shipping Packages The U.S.…

04:31

Shipping regulations A shi…

10:54

a. The U.S. Postal Service…

I have a lot going on this problem. So the first thing we need is a box with a square in despots. Six seconds Already been through the postal Service cleaning appear a little bit, all right. And they're telling us that we don't know the length of this. A pair of, like, measurement here. It tells us the girth. That's this area around it. So girth in actuality is pretty much the same thing as perimeter. All right, so they tell us this girth at mass could be 100 and eight inches. So 108 inches is less than using the idea of perimeter to s plus two. They tell us this ass is 18 inches. Our side is 18 inches. So it is so for else that multiply that by two, subtracted it from both sides two times 18 36. So subtracting that I get 72 is less than or equals that too, too. Well, divide both sides by two and 36 is less than or equal to. So we really could have done the spine equation. But we're leading into our inequalities here a little bit, but now they want to know is what's the maximum volume that I could get? All. So we're just going to use our volume equation and volumes equal to the base times height. Remember this basis, that area of the base. That's why it's a Capital B instead of a little B. Yeah, we could replace that h within out. You're right and already a substitute in. So we know that our base, if I may use that square, is 18 inches so that 18 inches squared and I'm gonna multiply that by my length, which I found it in a maximum of 36. Do the math like 11,664. Remember units inches cubed. And so our maximum value is 11,664 inches. Cute if we're using a box with a square base measuring 18 inches, Other measurements. Mike is awesome.

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