The management of the UNICO department store has decided to enclose an 891 ft2 a

Question

The management of the UNICO department store has decided to enclose an 891 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 $2/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal wood side ft steel side ft

Explanation / Answer

let length of side having pine board =x

length of side having galvanised steel fensing =y

total cost C=7(x+x) +2y

C=14x+2y

area enclose =xy =891

=>y=891/x

C=14x+2(891/x)

for minimum cost dC/dx =0 ,d2C/dx2>0

dC/dx=14 -2(891/x2)

14 -2(891/x2)=0

2(891/x2)=14

x2=2*891/14

x=11.282

x=11.3ft

y=891/x

y=891/11.282

y=78.9 ft

wood side =11.3 ft

steel side =78.9 ft

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