Thread: Differentiation Applications

So I am having some trouble with a certian type of question that has arisen in some of the past work I have done leading me to believe that it could appear in my upcoming examination. So on with the question:

A farmer plans to use a river as a one boundary of a rectangular paddock. If the farmer has 480m of fencing to be used to fence the remaining 3 sides, what dimensions should the paddock be to ensure maximum area.

Help is greatly appriciated.

Originally Posted by holmesb

...

A farmer plans to use a river as a one boundary of a rectangular paddock. If the farmer has 480m of fencing to be used to fence the remaining 3 sides, what dimensions should the paddock be to ensure maximum area.

Hello,

let w be the width of the rectangle and
l be the length of the rectangle.

Then the area is calculated by:

[1]

the fence f consists of . Since f = 480 you get:

[2]

Plug in the term for l into the equation [1]:



This is a parabola opening downward, the maximum value is at it's vertex:

and

You'll get: w = 120 m and l = 240 m. The maximum area is 28800 m²