A single-period market that contains a $100 risk-free bond with a bond rate of 7% and risky $50 stock. The rate of return on the stock is normally distributed with mean S= 2% and standard deviation oS = 10%. (a) State the expected return and associated risk (as measured by the standard deviation) in terms of w if w is the stock's weight allocation in the portfolio. (b) Suppose that the utility function used was u(x)=-e^(-0.001x) and the portfolio was constructed so that it's initial value was $2000 and the expected utility of future wealth was maximized. Determine the following: (i) The percentage of the portfolio's initial value invested in: w1 and w2 Use these values to solve parts (ii)-(iv). (ii) The number of: x and y (iii) The expected rate of return on the portfolio. (iv) The risk in the portfolio.