Consider the following problem max f(w) = ou w - (1 - a)w Pw subject to why =1 where o E (0, 1), A = [/1, /2, ..., An] are the expected rates of return of n different assets in a portfolio with weight vector w = [w1, w2, ...,w.] and covariance matrix P = PT > 0. (a) Find the value of w* that maximizes f(w) and state any conditions to be satisfied. (b) Use the results in (a) to find the optimum portfolio of 4 stocks with the following characteristics: #1 = 0.08, /42 = 0.10, /3 = 0.25, / = 0.05, 0; = 0.04, 03 = 0.06, 03 = 0.09, 070.009, 012 = 0.001, 013 = 0.008, 014 = 0, 023 = 0, 024 = 0, 034 = 0.002 If you have $1 million, how will you set up the portfolio