Question

We want to build a pen for sheep and we have 60 feet of fencing. We plan to build the pen next to the river so that we only need to include three sides. Find an equation for y in terms of x. Find the value of x that produces the largest total area?

Answer 1

By the condition of the problem total length of the fence building the rectangular pen is `60ft` which covers 3 sides of the rectangular pen.

So `y+2x=60`

The area of the rectangular pen

`A=xy=x(60-2x)=60x-2x^2`

`=>A=-2(x^2-30x)`

`=>A=-2(x^2-2*x*15+15^2-15^2)`

`=>A=15^2-2(x-15)^2`

A is maximum for `x-15=0`
Hence
A will be largest for `x=15ft` for which largest total area will be `225ft^2`