Problem $2.[15$ points$]$ You are the portfolio manager of a financial investment firm and you have a total of $\backslash (\backslash$$ $1,000,000\backslash )$ to invest. Your task is to allocate funds among three different investment options to maximize the expected return after five years. Please note that you can invest at the beginning of each year and the return of a completed investment can be invested again. The investment options with their expected profit and duration are given in the table below:

Formulate this problem as a linear programming model, and explain the decision variables, the objective function, and the constraints you write.