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)?
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x = __________
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y = __________
​
z = __________
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C = __________

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Definitions:

Efficient Market

A financial market theory suggesting that asset prices fully reflect all available information, making it impossible to consistently achieve higher returns than the average market return.

Cogito Ergo Sum

A philosophical statement by René Descartes, which translates to "I think, therefore I am," used to demonstrate the existence of the self and consciousness.

Carpe Diem

A Latin aphorism usually translated as "seize the day," encouraging individuals to make the most of the present moment without concern for the future.

Redistribution Of Income

The transfer of income from certain individuals or groups to others through mechanisms such as taxation, welfare, and government policies.