The management of the UNICO department store has decided to enclose a 914 ft 2 a
ID: 3346159 • Letter: T
Question
The management of the UNICO department store has decided to enclose a 914 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 $6/running foot and the steel fencing costs $4/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 steel length = S
Let one side of pine length = P
Area = P*S = 914
Cost = (2P)*6 + S*4 = 12P + 4S
C = 12P + 4S
or C = 12P + 4*914/P
Cost minimum for dC/dP = 0
=> 12 - 4*914/P^2 = 0
=> P = 17.45
S = 914/17.45 = 52.36 ft
Total pine used = 2P = 34.9 ft
Steel = 52.36 ft
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