be the amount invested in investment i. Let 
be the amount in the savings account. The objective is to maximize
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.