Question

1. 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.

Answer 1

Ans

let the investments in 1st, 2nd and3rd month be x1, x2, x3 respectively

money received (output) in year 1, 2 , 3 be y1, y2, y3 respectivly

here x1+x2 <=10000000

x1=2*x2

x2<=3330000

X1<=6670000

y3= 2*x1= 13340000

x3= y3* (2/3)

Here

The model is shown below with calcutions for maximizing the output:

	month 1	month 2	month 3	month 4	month 5	month 6	final encashment
investment	6670000	=F7/2	=H8*0.67	=H7/2	=J8*0.67	=J7/2
output			=F7*2		=H7*2		=J7*2

	month 1	month 2	month 3	month 4	month 5	month 6	final encashment
investment	6670000	3335000	8937800	4468900	11976652	5988326
output			13340000		17875600		23953304

Final encashment= 23953304