Question

A pig farmer wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle (see the figure below). There are 900 feet of fencing available to complete the job. What is the largest possible total area of the four pens?

The answer is not 40500 ft^2.

Answer 1

Area of rectangle A=xy

x-length of rectangle

y-width of rectangle

SINCE THEY ARE DIVIDED INTO 4 PENS , THEY CONSIST OF 5 WALLS MADE OF FENCES OF LENGTH x.

• Length of fence required = 900
• 5x+2y=900

The Area is the required function A=xy

To find critical points (derivative=0), to find area is maximum or minimum

To check whether it is maximum or minimum we take second derivative test

Since there is no x present, no changes occur to value.

• if second derivatives f"(x)>0, x is local minimum
• if second derivative f"(x)<0, x is local maximum

Therefore x=90 is maximum value.