The perimeter of the area of the pen the farmer intends to build for his
ship includes the length of the permanent stone wall.
Response:
i) The length and width of the rectangular pen are; <em>x</em>, and , therefore;
- The area is;
iii) The value of <em>x</em> that makes the area as large as possible is x = 50
<h3>How is the function for the area and the maximum area obtained?</h3>Given:
The length of fencing the farmer has = 100 m
Part of the area of the pen is a permanent stone wall.
Let <em>x</em> represent the length of the stone wall, we have;
2 × Width = 100 m - x
Therefore;
Width, <em>w</em>, of the rectangular pen,
Area of a rectangle = Length × Width
Area of the rectangular pen, is therefore;
, and
are found as follows;
iii) The value of <em>x</em> that makes the area as large as possible is given as follows;
Given that the second derivative, , is negative, we have;
At the maximum area, , which gives;
x = 50
- The value of x that makes the area as large as possible is <em>x</em> =<u> 50</u>
Learn more about the maximum value of a function here: