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 4 dollars per foot, and the material for t

Algebra ->  Volume -> 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 4 dollars per foot, and the material for t      Log On


   

Question 288373: 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 4 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the length L and width W (with W \leq L) of the enclosure that is most economical to construct.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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 4 dollars per foot,
and the material for the fourth side costs 15 dollars per foot.
Find the length L and width W (with W \leq L) of the enclosure that is most economical to construct.
:
Area equation:
L * W = 290
W = 290%2FL
:
Perimeter equation
P = 2L + 2W
:
Cost to enclose
C = 4(2L) + 4W + 15W
C = 8L + 19W
Replace W with %28290%2FL%29
C = 8L + 19%28290%2FL%29
C = 8L + 5510%2FL
:
Plot this equation, L is on the x axis, Cost on the y axis
+graph%28+300%2C+200%2C+-10%2C+40%2C+-200%2C+1000%2C+8x%2B%285510%2Fx%29%29+
Minimum cost when L = 26 ft
then
290%2F26 ~ 11.15 ft is the width
:
Check area: 26 * 11.15 = 289.9 ~ 290
Check cost: 4(2*26) + 4(11.15) + 15(11.15) = $419.85 is minimum cost