You have $140,000 to invest over three types of investment choices: bonds, a stock index fund, and gold. The current bond yield is 3%, the index fund is projecting a 9% return, and gold is projecting an 5% return. To play it safe, you want to keep no more than $55,000 in the index fund and at least four times as much in bonds as in gold. If the projected returns are accurate, how much should you allocate to each investment in order to maximize your return? Develop a mathematical and excel model to recommend the optimal solution.