$15.$ Investments: the prospectus of an investmnet fund states that all money is invested in bonds that are rated A$,$ AA$,$ and AAA; no more than $30\%$ of the total investmnet is in A and AA bonds, and at least $50\%$ is in AA and AAA bonds. The A$,$ AA$,$ and AAA bonds, yield $8\%,7\%,$ and $6\%,$ respectively, annually. Determine the $\%\text{'}$s of the total investment that hsould be committed to each type of bond so that the fund maximizes its annual yield. What is the yeild?