A rectangular pasture adjacent to a river has to be fenced with no fencing along the river. If the pasture must contain 245000 square meter in order to provide enough grass for the herd what dimensions will require the least amount of fencing?
The farmer has to create a rectangular pasture with an area 245000 square meter beside a river.
Let the side of the pasture perpendicular to the river be x, the other side is `245000/x` . If a fence is created around the pasture its length is `Y = 2*x + 245000/x`
To find the least value of Y, solve `(dY)/dx = 0`
=> `2 - 245000/x^2 = 0`
=> `245000/x^2 = 2`
=> `x = sqrt(245000/2)`
=> x = 350
This gives the dimensions of the pasture as 350 m and 700 m.