Solve using the graphical method of linear programming Felix and Maria Strom sold some property and decided to invest $$65,000$ in low$-$risk government bonds and in higher$-$risk corporate bonds. Their investment counselor suggested government bonds that paid $4\mathrm{.}4\%$ interest and corporate bonds that paid $6\mathrm{.}75\%$ interest. Felix and Maria wanted to be sure their investment included a balance of both bond types, so they instructed the investment counselor to invest at least $$15,000$ in government bonds and no more than $$32,000$ in corporate bonds. They wanted the maximum return on their total investment. Find the amount invested in each type of bond that will maximize interest income.