Question

The management of a department store has decided to enclose an 800 sq. ft.area outside the building for displaying potted plants and flowers. One side willbe formed by the exterior wall of the store, two sides will be constructed of pineboards, and the fourth side that is opposite to the wall will be made of galvanizedsteel fencing. If the pine board fencing costs $6/ft. and thesteel fencing costs $3/ft,determine the dimensions of the enclosure that can be erected at minimum cost

Answer 1

Dimension of the enclosure is 56.56 ft * 14.14 ft

Explanation:

Given -

Let us suppose that x is the length of steel fence and y is the length of one side of pine boards

We know that - xy = 800.

y = 800/x

Let us say that C is the cost of fence

= 3x + 6(2y) = 3x + 12y = 3x + 12(800/x)

C = 3x + 9600x-1, x > 0

C' = 3 - 9600x-2 = (3x2-9600)/x2

C' = 0 when 3x2 = 9600

x2 = 3200

x = √3200 ft ≈ 56.56 ft

So, the cost is minimized when x ≈ 56.56 ft and y = 800/x ≈ 14.14 ft