Patricia has at most $45,000 to invest in securities in the form of corporate stocks. She has narrowed her choices to three groups of stocks: growth stocks that she assumes will yield an 11% return (dividends and capital appreciation) within a year, speculative stocks that she assumes will yield a 13% return (mainly in capital appreciation) within a year and EFTs which average at 10% return per year. Determine how much she should invest in each group of stocks to maximize the return on her investments within a year if she has decided to invest at least 3 times as much in growth stocks as in speculative stocks and at least twice as much in EFTs as in growth stocks.

Hint: Total money is the only resource

*Please show the solution step by step. Thanks