Maximising Savings through Linear Programming

One of Warren Buffet’s Golden Rules about money was to ‘spend’ what is left after saving.


I thought I would dedicate a post regarding a mathematical method of optimising savings without having to curtail basic expenditure.


saving and spending
saving and spending (Photo credit: 401(K) 2013)


One of the ways to it can be done is a mathematical method known as ‘Linear Programming’. The method was said to be developed during the World War II when a need was felt to channelize resources strategically when they are in a short supply. ( A t that point of time, the main focus was to maximise damage to the enemy and minimize losses.)


An American Economist, G.B.Dantzig is credited for the term ‘Linear Programming’ and he formulated the general linear program problem which was published in the journal “Econometrics” in 1947.


Now, returning to the problem at hand, of optimizing (maximizing or minimizing) savings and expenditures.


Suppose, as a student I am earning Rs 20,000 a month freelancing and working part time and I am compelled to take care of entire finances.


I would like to organise my expenditure and plan it out carefully so that I can have a fixed amount of money laid by as savings every month.


The constraints to my monthly savings are rent, food, medical insurance/ education loan, miscellany (clothing, cable tv, internet, transport etc). The constraints are not fixed but are in a range. So if I can spread out the expenses and study the range, I can channelize the resources (money) within the constrains and keep my savings at a steady level.


Suppose, based on the trends of the last few months, I come to the following IN 4 DIFFERENT COMBINATIONS:


X1 + Y1  ≤8000


X2 + Y2 ≤(20,000-8000) OR X1/4 +Y2  ≤12,000


X1 +Y2 ≤ (10,000)


X2 + Y1 OR X1/4 +Y1 ≤6000




Graph 1- Linear Programming
Graph 1- Linear Programming


Interpretation of the graph:


When I get obtain a trend of how my basic and general monthly expenses are bracketed, my expenditures cannot exceed my monthly income as shown by the four combinations above.


This graph shows that the basic expenditure on “food and rent” is less than half of the total monthly expenditure. Even the combination of “Rent and miscellany” which consumes a lot of money does not exceed half of the total income. This graph shows that the various constraints can be plotted in different ways and we can still have a saving from the basic monthly income if we manage to derive a definite trend of expenditure and stick to it.


PART 2 is scheduled for tomorrow (14.03.13). Stay tuned!




You may also like:


The Budget Line


On Financial Discipline: A lesson I learnt from  a famous movie


Analyzing Choices While Buying


Game Theory-Determining Strategic Behaviour


Smart Shopping?


©The Idea Bucket, 2013



  1. I like the idea of course, but I don’t get how its done. I understand that I earn 20,000 per month, out of which I get to spend my monthly expenses which are expressed here as X1, X2, Y1, and Y2. I don’t understand the equations part. Why do we divide X1/4 ? And where is the remaining 4000 here:
    X1 +Y2 ≤ (10,000)
    X2 + Y1 OR X1/4 +Y1 ≤6000
    Its obvious I don’t get a thing.. Sorry! 🙂


    1. A. M. says:

      The equations are based on different combinations of the variables, X1, X2, Y1 and Y2. And to solve the problem, an interpretation of a trend is derived, for eg, I find that in my expenses, the value of variable X2 equals X1/4. Since, various forms of the expenses are shown in the equations, the sum will not be equal to my monthly income as a part of it is being saved. So it is to derive a trend in my expenses that keeps it in check and also allows me to achieve my saving-goals.
      I hope this has cleared your doubt. Thanks for the visit! 🙂


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