Consider the following problem max f(w) aw-(1-a)w Pw = subject to where a (0,1), w1, 1 (2) are the expected rates of return of n different assets in a portfolio with weight vector w (w, 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: =0.08, p = 0.10, 3 = 0.25, 13 0.008, 014 0,023 0,024 0.05, 0,034 = 0.002 0.04, 0 = 0.06,0 = 0.09, 0.009, 12 =0.001, If you have $1 million, how will you set up the portfolio?