Question

Explanation of the problem chapter 3.12 problem 49 of the book introduction to the mathematical programming 4th edition

Solution: Step # 1
Let Xij be the amount of money invested at the beginning of month i, for a period of j month.
Objective function: Step # 2
The objective is to maximize the available cash at the beginning of month 5.
X14 = collect the money invested at the beginning of month 1 of 4 months.
X23 = collect the money invested at the beginning of month 2 of 3 months.
X32 = collect the money invested at the beginning of month 3 of 2 months.
X41 = collect the money invested at the beginning of month 4 of 1 month.
Therefore the objective function is:
Maximize Z = 1.08 X14 + 1.03 X23 + 1.01 X32 + 1.001 X41
Restriction 1
It would be the money invested at the beginning of month 1 plus bills paid in month 1 which would be equal to the money available at month 1.

                       X11 + X12 + X13 + X14 + 600 = 400 + 400 (MONTH 1)
Restriction 2
It would be the money invested at the beginning of month 2 plus bills paid in month 2 which would be equal to the money available at month 2.

X21 + X22 + X23 + 500 = 1.001 X11 + 800 (MONTH 2)
Restriction 3 and 4
In the same way for the rest of the month we have:

X31 + X32 + 500 = 1.001 X12 + 1.001 X21 + 300 (MONTH 3)
X41 + 250 = 1.001 X13 + 1.001 X22 + 1.001 X31 + 300 (MONTH 4)

What I need is an explanation of the problem of how the data was extracted at each step

Answer 1