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Optimization Problem?

A rectangular bird sanctuary is being created with one side along a straight riverbank. The remaining three sides are to be enclosed with a protective fence. If there are 16 km of fence available, find the dimension of the rectangle to maximize the area of the sanctuary.

Please Help!

2 Answers

  • 2 months ago

    Help yourself. Draw a picture and puzzle through it manually, then learn the formula(s) you would use whenever you encounter this situation.  P S A half-circle would actually provide the most enclosed area.

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  • david
    Lv 7
    2 months ago

    A = lw

      let l = r --- the riverbank  .. which has one parallei side to be fenced

      16 = r + 2w

         r = 16 - 2w

      A(w) = w(16- 2w) = 16w - 2w^2

      A' = 16 - 4w = 0

       w = 4 km

      l = 16 - 2*4  =  8km

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