An investor wants to determine the safest way to structure a portfolio from several investments. Investment A produces an average annual return of 14% with a variance of .025. Investment B produces an average rate of return of 9% with a variance of .015 Investment C produces an average rate of return of 8% with a variance of .010. Investments A and B have a covariance of 0.00028 and investments A and C have a covariance of -0.006. Investments B and c have a covariance of 0.00125. Suppose that we need to decide the fraction of our money to put in investment A, B and C. Thus, we can simply use the decision variables A, B and C to denote the fraction (or percentage) of our money to put in investments A, B, and C respectively. Answer the following questions.

= [2A2 + 2B2 + 2C2 + 2*covariance*AB + 2*covariance*AC + 2*covariance*BC]^.5 (a) Suppose that the investor wants to achieve at least a 12% return. Develop an algebraic model to find the least risky way of doing this, using portfolio standard deviation as a measure of risk. (Recall that standard deviation () = square root of variance (2)).