An Investor Seeks to Create a Portfolio from Three Types

An investor seeks to create a portfolio from three types of securities: Treasury Bills (T), Corporate Paper (C), and Junk Bonds (J). The table lists the expected rates of return for the asset types and their average risk (on a 1-5 scale, where '5' denotes maximum risk). The investor seeks portfolio allocations (T + C + J = 1) that will maximize the expected return on her portfolio, while maintaining an overall risk of no more than '3'.
$\begin{array} { l c c } \text { Security } & \text { Return (\%) } & \text { Risk } \\\hline \text { Treasury Bills } & 2.5 & 2.0 \\\text { Corporate Papers } & 5.0 & 2.5 \\\text { Junk Bonds } & 8.0 & 5.0 \\\hline\end{array}$
(a) Formulate the investor's linear programming problem.
(b) Why will the investor’s portfolio contains only two assets? Determine the investor’s optimal portfolio. If the investor is willing to increase her portfolio risk by 1.0, how much does her return increase?