Sandra has at most $$200,000$ to invest in stocks, bonds, and money market funds. She expects annual yields of $15\%,10\%,$ and $8\%,$ respectively, on these investments. If Sandra wants at least $$50,000$ to be invested in money market funds and requires that the amount invested in bonds be greater than or equal to the sum of her investments in stocks and money market funds, determine how much she should invest in each vehicle to maximize the return on her investments.