Alice's preferences for good X and good Y are described by the following utility function:U(X, Y) = X + 2Ywhere X and Y are the respective amounts of the good X and good Y Alice consumes.

_ Compute the numerical values for Alice's optimal choices for good X and good Y. Show relevant steps and carefully explain your reasoning. Draw a graph that illustrates Alice's optimal choice in this case. 4. Now suppose that the price of good X is PX = 2 and the price of good Y is Py = 6. Suppose that Alice's income is I = 10. Compute the numerical values for Alice's optimal choices for good X and good Y. Show relevant steps and carefully explain your reasoning. Draw a graph that illustrates Alice's optimal choice in this case. 5. Alice returns from shopping with the bundle (X,Y) = (3,8). Without knowing anything about the current prices or Alice's income but knowing that X and Y are perfect substitutes for Alice, Alice's 'iend Sally states \"I see by your bundle that you didn't utility maximise today\". Discuss the validity of this statement