A rancher wants to fence in an area of 3000000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?

Question

anonymous · Answer

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anonymous · Answer

minimize $3x+2y$ subject the the constraint $xy=3,000,000$

anonymous · Answer

solve for $y$ and get $y=\frac{3000000}{x}$ then you can minimize 
$$f(x)=3x+\frac{6000000}{x}$$

anonymous · Answer

take the derivative, set it equal to zero and solve