Through some years John Smith has been growing his real state. He owns already several building complexes with approximately 120 apartments. Last year he paid in full his properties, so now he has no obligation other than taxes for the money that he received. His income from last year real state was $1,000,000 after taxes.

John is thinking about diversifying his investments. He talked to his financial advisor asking him what options he had to invest his money so he can have earnings in 4 years.

His financial advisor offered him the following options to invest his $1,000,000:

Investment A: It is only available for investment at the beginning of year 1. Each dollar invested in A at the beginning of a year 1, returns $0.5 at the beginning of year 2, and another $0.8 at the beginning of year 3.

Investment B: It is only available for investment at the beginning of year 2. Each dollar invested in B investment at the beginning of year 2 returns $1.25 at the begining of year 4.

Investment C: It is only available for investment at the beginning of year 1. Each dollar invested in C at the beginning of year 1 returns 1.35 at the beginning of year 4.

Investment D: It is only available for investment at the beginning of year 3. Each dollar invested in D at the beginning of year 3 returns $1.13 at the beginning of year 4.

Investment E: It is only available for investment at the beginning of year 1. Each dollar invested in E at the beginning of year 1 returns $1.27 at the beginning of year 3.

John's financial advisor also told Jhon that it is best to not place more than $500,000 in any single investment. And that he should keep at least $50,000 at the end of each year (remaining money should be at least $50,000 every year).

QUESTION. If you were John's financial advisor, how would you advise him to invest his earnings if he wants to maximize the amount of money he will receive at the beginning of year 4?

Formulate the above problem mathematically as a linear programming model. Define you decision variables clearly (define the notation you use) and use them to formulate the objective function and constraints. To do so, you can complete the following table with the investment's information (Green squares represent investment, orange squares represent remaining money for the year)

Solve the problem using solver and give an answer to the question above.