Question
Asked Nov 24, 2019
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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? 

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Expert Answer

Step 1

Let a and b are the dimensions of each field as shown in the below figure.

Thus, the area of each field is a × b.

Therefore, the dimensions of the rectangular plot are 3a and 2b.

Let A be the area of the rectangular plot then we have

            A = 6ab

а
b
2b
За
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а b 2b За

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Step 2

The perimeter of the rectangular plot is 2(2b + 3a)

Since the total fence available is 700 feet therefore the perimeter of the rectangular plot must be equals to the 700.

2(2b +3a) 700
700
2b +3a
2
2b 350-3a
350-За
2
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2(2b +3a) 700 700 2b +3a 2 2b 350-3a 350-За 2

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Step 3

Substituting the value of b in the expre...

А -D баb
350-За
А— ба
2
А - За
350-За
)
А 3D 1050а -9a?
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А -D баb 350-За А— ба 2 А - За 350-За ) А 3D 1050а -9a?

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Tagged in

Math

Calculus

Derivative