Please show working out/theory

There are three investors X, Y and Z whose preferences represented by the utility function U E(r)-0.52, where a is the risk-aversion coefficient, and is highest for X and lowest for Z. Based on the Markowitz's optimal portfolio theory, in the absence of a risk-free asset, an investor's optimal portfolio is the tangent portfolio of her utility indifference curve with the efficient frontier of the investment opportunity set. The graph below plots the efficient frontier, three investors' utility indifference curves, and the respective tangent poriolio What should be the optimal portfolios of the three investors X, Y and Z respectively