Suppose that income is M, and prices are P1 and P2, and consider the following utility function:

$\displaystyle U(x1,x2)=U(X_1X_2) = X_1^{0.4}X_2^{0.6}$

a. Using Lagrangian, derive the ordinary demand functions of $\displaystyle X_1$ and$\displaystyle X_2$.

b. Suppose M=$100, and prices are P1=$20 and P2=$20; calculate the utility maximizing quantities of $\displaystyle X_1 $and $\displaystyle X_2$. If price of good 1 drops to $10, what would be the demand for $\displaystyle X_1$. Using this infomation, draw a demand curve of $\displaystyle X_1$.

for a, do I just need to find the partial derivative of U with respect to $\displaystyle X_1$, and $\displaystyle X_2$, then divide $\displaystyle X_2$ by $\displaystyle X_1$?

and I need some hints on b