Homework

# Volume maximization-Calculus

Customer Question
A shelter for the beach...
A shelter for the beach has a back, 2 square sides and a top. Suppose that 250 square feet of canvas are to be used. Find the smallest dimension of the shelter for which the space inside the shelter (volume) will be maximized

I need to know all the steps to this. Thanks!
Submitted: 13 years ago.Category: Homework
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4/6/2005
Tutor: Hatice Ozer, Graduate Student replied 13 years ago
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we know that

total area is let say one side X

and height is h

total area= 2x^2+4xh=250

then total volume is

x^2*h

so that we know

h=250-2x^2

----------------

4x

then we will find the volume which is

V=x^2*(250-2x^2)

-----------------------

4x

V=(250x-2x^3)/4

we will take the derivative with respect to x and equat to 0

250=6x

x=125/3

so that the base side will be 125/3

Customer reply replied 13 years ago
Reply to Hatice Ozer's Post: So what is the smallest dimension? I know it's between 6 and 8 feet but just can't figure out what it is
Tutor: jacket, BS degree in math replied 13 years ago
jacket, BS degree in math
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jacket, BS degree in math
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Tutor: RoberttheRocket, Teacher/tutor replied 13 years ago
RoberttheRocket, Teacher/tutor
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whoa!

don't forget the h = 250 - 2x^2/4.

Since the h = 250 - 2x^2/4x

then t will equal (250 - 2(6.45497)^2 )/ 4(6.45497)

=  (250 - 83.333275) / 25.81988 = 6.45497 also

so the shape of the shelter will be a  cube.

Note:  I have a problem with this because the 250 square feet will cover the shelter (the sides, back, and top), but in the calculations, I see all six sides have been used for the surface area. (250 = x^2 + x^2 + 4xh.)

Tutor: xarqi, Generalist replied 13 years ago
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My assessment of the answers above:

Jacket's response is excellent.

RoberttheRocket's point is well made, but does not refer to

Site rules prevent me from commenting openly on the quality of
jacket, BS degree in math
Category: Homework
Satisfied Customers: 62
62 Satisfied Customers
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