The management of the UNICO department store has decided to enclose a 931 ft 2 a

Question

The management of the UNICO department store has decided to enclose a 931 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 $5/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 The management of the UNICO department store has decided to enclose a 931 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 $5/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.)

Explanation / Answer

let wood length be w, and steel length be s

s*w = 931

so w = 931/s

cost = 2*w*5 + 3s = 10w+3s

substituting w

cost = 10*931/s + 3s = (9310 + 3s^2)/s

for cost to be minimum, d cost/ds = 0

so d cost/ds = s*6s- (9310+3s^2)/s^2 = 0

so 6s^2 - (9310+3s^2) = 0

so s = 55.71 ft

so w = 931/s = 16.71 ft

wood side = 16.71 ft

steel side = 55.71 ft

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.