Homework Help: calculus

Posted by help please. on Monday, March 19, 2012 at 1:14pm.

An open rectangular box having a volume of 256 is to be constructed from a tin sheet.
Find the dimensions of such a box if the amount of material used in its construction is to be minimal.

Hint: Let the dimensions of the box be x by y by z . Then, xyz=256 and the amount of material used is given by . Show that f(x,y)= xy + 512/x + 512/y

minimize f(x,y)

calculus - Reiny, Monday, March 19, 2012 at 1:27pm
we know xyz = 256
so z = 256/(xy)

Surface area = SA
= 2xy + 2xz + 2yz
= 2xy = 2x(256/(xy)) + 2y(256/(xy))
= 2xy + 512/y + 512/x

hope that helps.

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