Hi Could anyone please provide me a detail work out for these questions?

Expected Utility and Optimal Portfolio. (11 marks) Consider another investor. She is risk averse, her utility of wealth is given by u (y) = In y. She considers states 1 and 2 equally likely, has initial wealth wo = 12 and has access to the financial markets with two risky financial assets a, and a2. Assets' state payoffs are given in the matrix 2 1 3 The prices of the assets (a1, a2) are q1 = 2, 92 = 3. a. (1 mark) Denote with > the amount of asset a, and with 22 the amount of asset a2. What is this investor's budget constraint, that is how much of these assets can she buy with her wealth of wo- b. (1 mark) What wealth levels (31, 92) can she reach in states 1 and 2 holding an arbitrary portfolio (21, 22)? c. (3 marks) Given the budget constraint in a. derive the trade-off between y1 and y2. (1 mark) Plot the resulting equation in (31, 32) space. (1 mark) How does the slope of this y2 (y1) line reflect the absence of arbitrage opportunities here? d. (4 marks) Derive the optimal portfolio for this investor. Hint: you should maximize the expected utility U (31, y2) subject to the trade-off between y and yz derived in c. Your optimal portfolio should be the optimal combination (21, 22) . You can approach this optimization problem with a Lagrangean