Suppose a consumer has the following utility function: U=X" if P,=2 and P.T=1 and Income = 150 1) Find the optimum quantitics of X and that the consumer will purchase. (8 marks) {In your solution you should begin by stating the two conditions that must be met.) 2} Why is this combination of X and an equilibrium? (2 marks) 3) What is the maximum satistaction that this wtility-maximizing consumer can achieve? (3 marks) Y 4) Hustrate the solution on the diagram. (2 marks)