utility function

For any given stockX, let µX denote its mean and s2X its variance. Assume an investor has utility function,u(X) =µX-s2X, and has a budget of $1 to
allocate between stocksA,B with mean, standard deviation as follows (i) µA=2, sA= 1, (ii) µB= 4, sB= 2. Also assume that ?A,B=-1, i.e. the stocks are perfectly negatively correlated. Assume bothA,B cost $1 per share and that shares are in?nitely divisible, i.e. you can buy any fractionaof a share. Compute the utility-maximizing portfolio choice of the investor. Assume the market for risk-free assets is perfect. What is the risk-free rate?