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Solve the following optimization problem:
Given $p=(p_1,p_2)\geq0$ and $c_1<0$, $c_2>0$\

max$\{ p_1x_1+p_2x_2 : c_1\leq x_1\leq 0; 0\leq x_2\leq c_2\sqrt[]{-x_1} \}$

I need an idea to solve the system

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