SOLUTION: A 1000 square yard rectangular lot along a highway is to be fenced off such that one side of the fence is on the highway. The fencing on the highway cost Php80 per yard and the fen
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Question 1193514: A 1000 square yard rectangular lot along a highway is to be fenced off such that one side of the fence is on the highway. The fencing on the highway cost Php80 per yard and the fencing on the other sides costs Php20 per yard. Determine the dimensions of the lot that will minimize the total cost of the fencing. Answer by ikleyn(52778) (Show Source):
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A 1000 square yard rectangular lot along a highway is to be fenced off such that
one side of the fence is on the highway. The fencing on the highway cost Php80 per yard
and the fencing on the other sides costs Php20 per yard.
Determine the dimensions of the lot that will minimize the total cost of the fencing.
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Let x be the length along the highway, in yards.
Then the length perpendicular to it is yards.
The cost of the fence is = .
They want you find the minimum of this function.
Take the derivative and equate it to zero. You will get this equation
100 =
which implies
100x^2 = 40000
x^2 = 40000/100
x^2 = 400
x = sqrt(400) = 20 yards.
ANSWER. The optimal dimensions of the lot are 20 yards along the highway and 1000/20 = 50 yards in perpendicular direction.
