Two stocks have returns per share X and Y; buying s shares of the first and t shares of the second results in a portfolio with returns Z=sX+tY. Suppose that E(X)=E(Y)=20, Var(X)=1, Var(Y)=2 and cov(X,Y)=1/2. a. An investment manager wishes to balance risk and reward by forming a portfolio which maximizes E(Z)3Var(Z). Find the optimal choices of s and t. b. A client tells the manager that they have a strict risk tolerance; they won't consider portfolios with variance more than 10 and would like to maximize their returns subject to this constraint. Find s and t so that E(Z) is maximized subject to the constraint Var(Z)=10