An Open Rectangular Box Having a Volume of Is

question 182

Essay

An open rectangular box having a volume of 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 = 108 and the amount of material used is given by S = xy + 2yz + 2xz. Show that Minimize f(x, y)
x = __________
y = __________
z = __________

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Definitions:

Attraction To Sweet

A natural preference or inclination towards sweet tastes, which is thought to have evolutionary origins.

Fat Tissue

Specialized biological tissue composed of adipocytes (fat cells) that store energy in the form of lipids.

Lean Tissue

Body tissue that is composed of muscle, organs, and bones, excluding fat.

Set Point

A theory suggesting that the body is programmed to maintain weight around a biological predetermined point, influencing appetite and metabolism.