hree different investment options are available at the beginning of each year during the next 6-year period. the durations of the investments are 1 year, 3 years, and 5 years. the 1-year investment yields a total return of 5.1%, the 3-year investment yields a total return of 16.2%, and the 5-year investment yields a total return of 28.5%. if an initial investment of $10,000 is made and all available funds are invested at the beginning of each year, formulate a linear programming model to determine the investment pattern that results in the maximum available cash at the end of the sixth year. furthermore, code and solve the problem in python following the instruction in this homework.