Francisco is planning to invest up to $$31,000$ in corporate and municipal bonds. The least he is allowed to invest in corporate bonds is $$7000,$ and he does not want to invest more than $$23,000$ in corporate bonds. He also does not want to invest more than $$17,000$ in municipal bonds. The interest is $6\%$ 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?

Francisco should invest $ $$ in corporate bonds and $ $$ in municipal bonds in order to maximize his income.