A senior executive of a public sector company recently quit his job under the VRS with a hefty packet of INR 1 Crore. Ms. Dhana-chor Chit Fund Company has offered the following investment scheme for the benefit of such retired people:

"Invest a certain sum (in lakhs of rupees) in any month; invest half of that amount in the next month. In the subsequent month, one would get twice the amount invested originally in the first month". This scheme is available only for the next six months (Encashment is possible on 181st day). Returns received at the end of any month can be used immediately for reinvesting either as a fresh investment or as a follow-up investment. Develop a mathematical model to optimize the investment strategy.