A Building in the Shape of a Rectangular Box Is

question 163

Short Answer

A building in the shape of a rectangular box is to have a volume of 21,000ft³ (see the figure). It is estimated that the annual heating and cooling costs will be $2/square foot for the top, $7/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)?
​ ​
x = __________
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y = __________
​
z = __________
​
C = __________

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Definitions:

Biome

A large, relatively distinct terrestrial region characterized by a similar climate, soil, plants, and animals, regardless of where it occurs on Earth.

Sympatric Speciation

The process of speciation that occurs when different species evolve within the same geographical area without physical barriers.

Geographical Region

An area of the Earth's surface characterized by distinctive physical, biological, and environmental conditions, often defined by natural or political boundaries.

Population

A group of individuals of the same species living in a particular geographic area and capable of interbreeding.