SOLUTION: A rectangular field having an area of 2700 m^2 is to be enclosed by a fence, and an additional fence is to be used to divide the field in the middle. The cost of the fence down the

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Question 453862: A rectangular field having an area of 2700 m^2 is to be enclosed by a fence, and an additional fence is to be used to divide the field in the middle. The cost of the fence down the middle is $24 per running meter, and the fence along the sides cost $36 per running meter. Estimate the dimensions of the field so that the total cost of the fencing material is least.

Answer by ankor@dixie-net.com(15660) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangular field having an area of 2700 m^2 is to be enclosed by a fence, and
an additional fence is to be used to divide the field in the middle.
The cost of the fence down the middle is $24 per running meter, and the fence
along the sides cost $36 per running meter.
Estimate the dimensions of the field so that the total cost of the fencing material is least.
:
the area
L * W = 2700
L = 2700%2FW
:
The perimeter
p = 2L + 2W + W; (3rd width down the middle)
Cost = 36(2L) + 36(2W) + 24W
C = 72L + 72W + 24W
C = 72L + 96W
Replace L with 2700%2FW
C = 72*2700%2FW + 96W
C = 194400%2FW + 96W
Graph this:
+graph%28+300%2C+200%2C+-20%2C+80%2C+-1000%2C+15000%2C+96x%2B%28194400%2Fx%29%29+
:
looks like min cost occurs when the width is 45 meters
then
length = 2700/45 = 60 meters
therefore
36(2*60) + 36(2*45) + 24(45) = $8640 is the min cost