Help!!! I have a math question and need help?

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  • A farmer has 600 ft of fencing to be used in the construction of of two identical rectangular pens sharing a common side.

    (a) Express the total area A(x) enclosed by both pens as a function of the width x.

    (b) From the physical considerations, what is the domainof the function A?

    (c) Find the dimensions of the pens that will make the total enclosed area maximum.


  • c


  • c


  • C. Definatly! I am sure!


  • c


  • The x be each of the 3 parallel sides (one of these is the common side).
    Then in the other direction the full length of the two plots together is (600-3x)/2. So.

    (a) A(x) = x(600-3x)/2 = 300x - (3/2) x^2

    (b) Domain of A is all x such that x>0 and 600-3x >0, i.e. 0 < x < 200.

    (c) A'(x) = 300 -3x = 0, so x=100, and (600-3x)/2=300/2=150. Since 150 is the lengh of the two adjacent pens together, each is 150/2 = 75. Thus:
    each pen is 100 feet by 75 feet.







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