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 ft^2 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

solution:

let the sides of the rectangular departmental store be x and y

the

xy=890

now

suppose length x walls cost 7/ft

and y 5/ft

then

cost=2x(7) +y(5)

and

y=890/x

putting here to get cost function

C=14x+890(5)/x

dC/dx=0

differentiating this

14-890*5/x^2=0

x^2=890*5/14=317.8

x=17.8

hence y=49.94

hence wood side=17.84 ft

steel side=49.94 ft

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