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.

Answer 1

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

Answer 2

960