Let the rate of return on the portfolio be R with expected rate of return and variance Op. Assume the investor's expected utility is expressed by the following function. V(R) = p 0, = E[R] Var[R], a > 0, Op 2 2 where "a" represents index of risk aversion. = Now there are J risky securities in the economy, and their rates of returns are expressed by the vector R with expected rates of return vector E[R] and covariance matrix 2. Assuming there exists an inverse matrix , and risk-free asset is not available for investment, answer the following questions. 1) Let the portfolio weights vector be w, and formulate the optimization problem that solves for the optimal vector w* which maximizes the expected utility. 2) Solve for the optimal weights vector w* by the method of Lagrange. Do not forget to eliminate the Lagrange multipliers from the solution.