Calculate the optimal quantities of X and Y that Ronald should choose, economics homework help

Ronald consumes two goods, X and Y. He has a utility function given by the expression: U = 2X^0.5Y^0.5.

So, MU_X = (Y^0.5) / (X^0.5) and MU_Y = (X^0.5) / (Y^0.5). The current prices of X and Y are 20 and 80, respectively. Ronald currently has an income of 640 per time period.

a. Calculate the optimal quantities of X and Y that Ronald should choose, given his budget constraint. Show your work.

b. Holding Ronald’s income and P_Y constant at $640 and $80 respectively, find out the equation for Ronald’s demand curve for X. Show your  work.