A Building in the Shape of a Rectangular Box Is

question 32

Short Answer

A building in the shape of a rectangular box is to have a volume of (see the figure). It is estimated that the annual heating and cooling costs will be $2/square foot for the top, $5/square foot for the front and back, and $3/square foot for the sides. Find the dimensions of the building that will result in a minimal annual heating and cooling cost. What is the minimal annual heating and cooling cost(C)?
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Definitions:

2-Ketohexose

A category of hexose sugars characterized by having a ketone functional group in the second position of the carbon chain.

NaBH4

Sodium borohydride, a chemical compound used as a reducing agent in organic synthesis.

Alditol

A type of sugar alcohol formed by the reduction of the aldehyde or ketone group in monosaccharides.

L-Erythrose

A four-carbon sugar, or tetrose, with the chemical formula C4H8O4, one of the simplest aldose configurations.