SOLUTION: A fence is to be built to enclose a rectangular area of 290 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for

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Question 293795: A fence is to be built to enclose a rectangular area of 290 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the length and width (with ) of the enclosure that is most economical to construct.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A fence is to be built to enclose a rectangular area of 290 square feet.
The fence along three sides is to be made of material that costs 3 dollars per foot,
and the material for the fourth side costs 15 dollars per foot.
Find the length and width (with ) of the enclosure that is most economical to construct.
:
Area: L * W = 290
W = 290%2FL
:
Cost:
C = 15L + 3L + 3(2W)
C = 18L + 6W
Replace W with 290%2FL
C = 18L + 6(290%2FL)
C = 18L + 1740%2FL
:
Plot this equation, cost on the vertical, Length on the horizontal
+graph%28+300%2C+200%2C+-6%2C+16%2C+-100%2C+1000%2C+18x%2B%281740%2Fx%29%29+
:
Minimum cost occurs when Length = 10 ft, then 290%2F10 = 29 ft is the width