I am really stuck with this problem, maybe somebody could help me out.

A rancher has 2100 feet of fencing with which to construct adjacent, equally sized rectangular pens as shown in the figure above. What dimensions should these pens have to maximize the enclosed area?

This is a picture that belonged to it as well.




Maximum area=

Thanks for your help!


  • 1
    $\begingroup$ You need to set up two formulas: First one is perimeter (related to fencing) and second one is Area. Can you do that? $\endgroup$ – imranfat Nov 14 '16 at 16:33

The perimeter of the figure is $P = 4x + 3y = 2100$.

The function to maximise is $A = 2xy$. Expressing the function to maximise in terms of a single variable(say x),

$$A = 2x(\frac{2100-4x}{3})$$. Can you complete the solution(using either calculus or using the point of maxima for a downward quadratic) ?

  • $\begingroup$ Thank you for your help. I was able to figure out that x= 525/2 or 262.5 But I'm having a struggle rewriting the formula used in terms of y. Can you help? $\endgroup$ – Franky Nov 14 '16 at 17:05
  • $\begingroup$ There is no need of rewriting the formula in terms of $y$. You know a direct relation between $x$ and $y$. $\endgroup$ – Shraddheya Shendre Nov 14 '16 at 17:33

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