Given function U(C,H)=C^2H. Advise how to maximise utility from two goods (C&H) given that price of both =200?

money to spend is 350. Also calculate quantities demanded for both C %26amp; H.

Given function U(C,H)=C^2H. Advise how to maximise utility from two goods (C%26amp;H) given that price of both =200?
The consumer's problem is to choose the quantities of the two goods that maximize his utility subject to his budget constraint. The solution to this problem is the combination of the two goods at which (1) the ratios of marginal utility to price for the two goods equal one another and (2) the budget constraint is binding, These conditions are represented by the respective equations:





(1) MUc/Pc=2CH/200=C^2/200=MUh/Ph, where Pc and Ph are the prices of the goods, and (2) 200C+200H=350.





The first equation requires that 2CH=C^2 or C=2H. Substituting this equation for C into the equation (2) above yields 400H+200H=600H=350, which implies that H=350/600=7/12 units of H is the utility maximizing quantity of that good. Finally, substituting this solution into the requirement that C=2H implies that C=2(7/12)=7/6 units of C is the utility maximizing quantity of that good.