John has a weekely endowment of $140 that he spends on buying games(G) and music cds(M). The price of each game is $30, the price of each cd is $20. He can buy any amount of the two goods that satisfies the budget constraint, including fractions (for example G=0.3987 and M=0.8765 is allowed as long as it is feasible). John's utility is given by:
U(G,M) = G^0.5 + M^0.5
a) find John's Budget constraint.
b) Set up the Lagrangian and find his optimal consumption.
c) What is his new consunption if the price of games becomes $20?