The management of the UNICO department store has decided to enclose an 890 ft 2

Question

The management of the UNICO department store has decided to enclose an 890 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 $7/running foot and the steel fencing costs $5/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 The management of the UNICO department store has decided to enclose an 890 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 $7/running foot and the steel fencing costs $5/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)

Explanation / Answer

let x be the length of wood side and y be on steel side, so total cost here c=2(7x) +5y given that xy = 890 so y = 890/x hence c= 14x + 5*890/x = 14x + 4450/x for c to be minimum , dc/dx = 0 so 0=14 - 4450/x^2 means x^2 = 317.86 means x = 17.829 so y = 890/x = 49.919 so wood side = 17.829 ft and steel side = 49.919 ft

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