Hi. I need some help with both of these questions. Full working out would help me a lot. Thanks

4.3. The following utility functions are defined over three goods, x, y, and z. Calculate the demand functions for each good, h; for j = x,y,z, as functions of the prices Px. Py, pz and income m. (a) u(x,y,z) = xyz (b) u(x,y,z) = x + In y +Inz Show that the demand functions satisfy the budget exhaustion prop- erty in each case, i.e., Pxhx+pyhy + pzh2 = m. 4.4. Ali spends his income of $64 on kerosene (x) and food (y) each week. The price of food is $8 per unit. The price of kerosene is $4/liter at a government-run store and he can purchase up to 8 liters there. On the market, kerosene costs $8/liter. His utility function is Cobb-Douglas: u(x,y) = xy? How much kerosene and food does he buy given his budget constraint