Kathleen Allen, an individual investor, has $$70,000$ to divide among several investments. The alternative investments are municipal bonds with an $9\%$ annual return, certificates of deposit with a $5\%$ return, treasury bills with a $6\%$ return, and a growth stock fund with a $13\%$ annual return. The investments are all evaluated after $1$ year. However, each investment alternative has a different perceived risk to the investor; thus, it is advisable to diversify. Kathleen wants to know how much to invest in each alternative to maximize the return.

The following guidelines have been established for diversifying the investments and lessening the risk perceived by the investor:

No more than $20\%$ of the total investment should be in municipal bonds.

The amount invested in municipal bonds should not exceed the amount invested in the other three alternatives.

At least $30\%$ of the investment should be in treasury bills and certificates of deposit.

More should be invested in CDs and municipal bonds than in treasury bills and the growth stock fund, by a ratio of $1\mathrm{.}2$ to $1.$

Kathleen wants to invest the entire $$70,000.$