Asked Nov 22, 2019

A farmer needs to take a rectangular plot of land and divide it into 6
fields of equal area. He has 700 feet of fence available to divide up this plot of land. What will be the dimensions for one of the fields if he wants to maximize the total area of the 6 fields?


Expert Answer

Step 1


First of all, construct the diagram as per the question.

Let, l = length of the field.

 b = breadth of the field.

The field is divided into six equal squares.

 a = side of a square.

Step 2


Now, total length of the fence is 700 feet to divide the land into six equal square.

So, the total perimeter of the square will be considered excluding the exterior perimeter because fence is not used to surround the land.

length of fence required to devide 700 ft
3a 2a 2a 700
7a 700
a 100 ft

Image Transcriptionclose

3a length of fence required to devide 700 ft 3a 2a 2a 700 7a 700 a 100 ft

Step 3

Now from diagram get the constrains.

And from the question get t...

bs 200

Image Transcriptionclose

Is3a 3(100) I300 bs2a 2(100) bs 200 Z=1xb


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