Anonymous
Anonymous asked in Science & MathematicsMathematics · 6 years ago

The management of the UNICO department store has decided to enclose an 847 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 \$3/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

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Lv 5
6 years ago

w*s=847 or s=847/w

Cost=14w+3s

C=14w+3(847/w)=(14w^2+2541)/w

dc/dw=14-2541/w^2

The cost will be minimized when dc/dw=0...

14 - 2541/w^2 = 0

14 - 2541/w^2 = 0

-2541/w^2 = -14

-2541 = -14 w^2

w^2 = 2541/14

w=+/-√2541/14=13.47

The wood sides are 13.5 feet

The steel side is 847/13.5=62.7 feet

The cost is 13.5*2*7+62.7*3=\$377.10