Utility maximization under constraint, substitution and income effect, CV and EV

Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 3[A3 + B3 ] 3 + 50. While Josh would like to consume as much as possible he is limited by his income.

a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method

b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain .

c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EV.