dimensions math question?

The management of the UNICO department store has decided to enclose an 863 ft^2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost.

Sqdancefan2016-10-14T12:13:53Z

Let x represent the length of the galvanized steel fencing. Then 863/x will be the length of each side. Total cost (c) of the enclosure will be
.. c = 2x + 7*2*863/x
Differentiating, we get
.. dc/X = 2 -14*863/x^2
.. x^2 = 7*863
.. x ≈ 77.724
.. 863/x = 11.103

The enclosure will be 77.724 ft wide (with steel fence) and 11.103 ft deep (with pine board fence).
_____
Note that the cost of each type of fencing is the same. This cost split is the general solution to a problem of this nature.

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