A couple wants to invest up to $$24,000.$ They can purchase corporate bonds yielding a $11\mathrm{.}85\%$ return on the amount invested and municipal bonds yielding a $15\mathrm{.}35\%$ return on the amount invested.

They want to invest at least as much in the corporate bonds as in the municipal bonds. They will also want to invest no more than $$13,000$ in the municipal bonds.

How much should they invest in each type of bond to maximize the return on investment?