Jerry has recently received some inheritance of $500,000 from a family trust fund. He wants to decide how to invest this $500,000. Jerry is considering investing this $500,000 on these four possible investment options: a technology stock, an oil stock, a mutual fund, and a one-year certificate of deposit (CD). Jerry estimates the return on the technology stock to be about 7.5% and the oil stock to be 9%. The mutual fund has a return rate of 12%. The CD has a 5.5% return rate.

To diversify his investment, Jerry would like the following setups for his investment:

1) The combined investment on the two stocks (technology and oil) cannot be more than $330,000.

2) At least $115,000 must be invested in CD.

3) No more than $185,000 should be invested in the mutual fund.

4) The investment on the technology stock should be at least twice as much as the investment on the oil stock

Like most investors, Jerry wants to maximize the return of his investment.

Set up a linear program to help Jerry with his investment decision. Clearly define your decision variables and list your objective function and the constraints. You do NOT need to solve your linear program.

Please show how you derive your answers and support your answers with correct explanations.