Question 1083120: A dairy farm has a barn that is 150 feet long and 75 feet wide. The owner has 240 feet of fencing and plans to use all of it in the construction of two identical adjacent outdoor pens, with part of the long side of the barn as one side of the pens, and a common fence between the two. Find the dimensions for the pens that maximizes the size of the pens.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! There is one long side x (it helps to draw this)
There are 3 short sides, one at each end, and one separating the two identical pens.
The 3 short sides are (240-x)/3 in length.
The area is x(240-x)/3=(240x-x^2)/3
The derivative is (1/9)(3)(240-2x), and set it equal to 0, so that multiplying by 9 removes it and dividing by 3 removes it, too.
240-2x=0
x=120 feet, the long side
Each short side is 40 feet.
Two pens are each 120*40=4800 ft^2
can try 41 and 117 as a check, and that area is 4797 ft^2
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