How to find Marshallian demand of $u(x,y,z)=x+y^2+2z^2$? Consider the utility function $u(x)=x+y^2+2z^2$. How to derive Marshallian demand for a consumer with these preferences?
Just compare the utilities of these three bundles: $\left(\frac{M}{p_X}, 0, 0\right)$, $\left(0, \frac{M}{p_Y}, 0\right)$ and $\left(0,0, \frac{M}{p_Z}\right)$ and consume the one that yields highest utility.