Write a linear programming model, including the objective function and the set of constraints, for Problems 52-55. DO NOT SOLVE, but be sure to define all your variables.

Brown Bros., Inc. is an investment company doing an analysis of the pension fund for a certain company. The fund has a maximum of \(\$ 10\) million to invest in two places: no more than \(\$ 8\) million in stocks yielding \(12 \%\), and at least \(\$ 2\) million in long-term bonds yielding \(8 \%\). The stock-to-bond investment ratio cannot be more than 3 to 1 . How should Brown Bros. advise its client so that the investments yield the maximum yearly return?