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I have the following maximization problem

$ \max_h m_1 + 10 (h)^{1/4} + h + m_2 - 2 (h)^{1/4} + m_3 - (h)^{1/4} $

where $m_1, m_2, m_3$ are three fixed values. The FOC for a maximum is

$ \dfrac {10}{4} h^{-3/4}+1-\dfrac{1}{2}h^{-3/4}-\dfrac{1}{4}h^{-3/4}=0$


$\dfrac{7}{4} \cdot h^{-3/4} = -1$

Well, now I have no idea... how can I go on? How can I say which level of $h$ maximizes my problem? Of course, I don't want you to solve, but I just would like to get a hint! Thank you in advance!

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what is $h$?is it function? – dato datuashvili Jul 21 '12 at 9:26
I just have to maximize that function with respect to $h$ – Luigi Jul 21 '12 at 9:33
up vote 1 down vote accepted

Are you saying you want help solving $$(7/4)h^{-3/4}=-1$$ If so, multiply by $4/7$, take reciprocals on both sides, raise both sides to the power 4, and take the cube root on both sides.

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