# Optimization with a constraint: An LP problem

Below problem is one that I'm drawing a blank on for even setting up the equation. Any help would be greatly appreciated.

Smith recently inherited a large sum of money; he wants to use a portion of this money to set up a trust fund for his two children. The trust fund has two investment options: (1) a bond fund and (2) a stock fund. The projected returns over the life of the investments are 6% for the bond fund and 10% for the stock fund. Whatever portion of the inheritance he finally decides to commit to the trust fund, he wants to invest at least 30% of that amount in the bond fund. In addition, he wants to select a mix that will enable him to obtain a total return of at least 7.5%.

What is the value of the optimal solution, i.e., the value of the objective function once you have determined the values of decision variables?

Â© BrainMass Inc. brainmass.com December 15, 2022, 4:25 pm ad1c9bdddfhttps://brainmass.com/math/algebra/optimization-with-a-constraint-an-lp-problem-24087

#### Solution Summary

The following outlines the process of determining the objective function and constraint then demonstrates the process of finding the constrained optimum.