The management of the UNICO department store has decided to enclose an 814 ft2 a
ID: 3186867 • Letter: T
Question
The management of the UNICO department store has decided to enclose an 814 ft2 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 $4/running foot and the steel fencing costs $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)
wood side (ft)
steel side (ft)
Explanation / Answer
let the length wood side be x(pine),breadth y(Steel). cost = 2x*4 + y * 2 = 8x + 2y xy = 814 => y = 814/x Substitute in the above equation. cost = 8x + 1628 /x = (8x^2 + 1628)/x When cost is maximum d(cost)/dx = 0 Hence 16x^2 - (8 x^2+1628) => 8*x^2 = 1628 => x = 14.5 dimensions are 14.5 feet of wood side and 56.13 feet of steel side
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