A javalina rancher wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. He has 470 feet of fencing available to complete the job. What is the largest possible total area of the four pens?

Question

jim766 · Answer

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Draw the diagram, label the side with parallel fencing should be x and there should be 5 of them. Since he has 470 ft of fencing available, the other side is (470-5x)/2. Now you have length and width to find area:
 
A(x) = x[(470-5x)/2] = 235x - (5/2)x²
 
Take the first derivative and set to 0:
 A'(x) = 235 - 5x = 0
 5x = 235
 x = 47
 There's the length of one side and the parallel fencing. The other side is 117.5, so the largest possible area:
 47(117.5) = 5522.5 sq. ft.

anonymous · Answer

Thank you!