Question

The management of the UNICO department store has decided to enclose a 917 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

Answer 1

assuming the fenced area is rectangular,
Let steel side be x, wood side be y

xy = 917, so
y = 917/x

The cost of the fence is thus

c(x) = 5x + 2*7(917/x)

Then find where c'(x) = 0

Answer 2

The management of the UNICO department store has decided to enclose a 855 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 $2/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