Francisco is planning to invest up to $$30,000$ in corporate and municipal bonds. The least he is allowed to invest in corporate bonds is $$5000,$ and he does not want to invest more than $$27,000$ in corporate bonds. He also does not want to invest more than $$6000$ in municipal bonds. The interest is $4\%$ on corporate bonds and $2\frac{1}{4}\%$ on municipal bonds. This is simple interest for one year. How much should he invest in each type of bond in order to maximize his income? What is the maximum income?