How can I solve a Lagrangean mimization problem with a CES constraint?

[jsgazevedo (jsgazevedo Azevedo)]

How to write a Mathematica 10 code for a solution of

[ScriptCapitalL]= ([Omega]*L+[Rho]*K) - [Lambda]*(Y-[Beta]*(!(
*UnderoverscriptBox[([Sum]), (j = 1), (n)](
*SubscriptBox[([Alpha]), (j)] 
*SubsuperscriptBox[(X), (j), ([Rho])])))^(1/[Rho]))