A consumer has set a budget of $200 for the consumption of good X and Y. The price of Good X is $40, and the price of good Y is $10. The consumer has a Utility function given by U(X,Y) = x3y

a) Find the optimal consumption choice of the individual and the utility obtained. b) Make a graph that illustrates the solution to the problem. c) Briefly express in writing the process that you used to find the solution. d) Discuss some of the possible limitations of the Consumer Choice Model when it comes to predicting the behaviour of consumers.