Model

Let the investments be numbered 1...5, and let be the amount invested in investment i. Let be the amount in the savings account. The objective is to maximize

subject to

Now, let's look at the average risk. Since we want to take the average over only the invested amount, a direct translation of this constraint is

This constraint is not linear, but we can cross multiply, and simplify to get the equivalent linear constraint:

Similarly we need

or

The final constraint is

Together with nonnegativity, this gives the entire formulation.