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’.

Security Return (%) Risk

Treasury Bills 2.5 2.0

Corporate Papers 5.0 2.5

Junk Bonds 8.0 5.0

Formulate the investor’s linear programming problem. You do not need to solve this. Write down objective and constraints.