You have $15,000$ to invest and have identified three options, shares in a new top $100$ tech company which is considered as high risk, an established top $100$ financial company considered as medium risk and gold which is considered low risk. You decide that your investment in gold will be twice as much as the investment in the two top $100$ companies combined. In addition you decide to invest $7,000$ in gold and the established top $100$ medium risk company. In addition at least $6,000$ will be invested in the established top $100$ medium risk company and the new top $100$ high risk company. The return expected is $6\%$ for low risk gold, $7\%$ for medium risk established top $100$ company and $12\%$ for high risk new top $100$ company. Formulate a linear programme to maximise your return. Solve the problem using software of your choice. Fully interpret your solution.