Corner time mon ami.

I have no idea why a problem of optimization under constraint is posed in algebra, but constraints may, and usually do, affect the answer. Moreover

** the problem is badly worded** because, as given, there is no indication what, if any, constraints are placed on the shape of either pasture. I don't know how to solve this problem without limitations on the geometry; it may require calculus of variations or some even more advanced technique.

If we set up two adjacent semicircles of equal diameter divided by a diameter fence, the cost

equation is

[tex]3 * \pi d + 2d = 4800 \implies d = \dfrac{4800}{3 \pi + 2} \implies[/tex]

the combined area is

[tex]\pi \left ( \dfrac{2400}{3 \pi + 2} \right )^2 \approx 138,636[/tex],

which considerably exceeds the area formed by rectangles.

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