Question
A fence must be built in a large field to enclose a rectangular area of 25,600m^2. One side of the area is bounded by n existing fence, so no fence is needed for that side. Materials for the fence cost $3 per meter for the two ends and $1.50 per meter for the side opposite of the existing fence. Find the cost of the least expensive fence.
Answers
If the ends are x and the other side is y,
xy = 25600
So, the cost
c(x) = 3*2x + 3/2 y
= 6x + 38400/x
so,
dc/dx = 6 - 38400/x^2
dc/dx=0 when x=80
So, plug that in and find the minimum cost
xy = 25600
So, the cost
c(x) = 3*2x + 3/2 y
= 6x + 38400/x
so,
dc/dx = 6 - 38400/x^2
dc/dx=0 when x=80
So, plug that in and find the minimum cost
960
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