0Since the very beginning, we tend to solve problems using mathematical mapping in our brain. Like in how many minutes will we reach the destination at this speed? Or, What will be the interest in a particular sum of money?
But often, complex real-life problems require mathematical solutions with the help of Mathematical Modelling. Examples :
- launching a satellite
- predicting the arrival of monsoon
- reducing traffic jams in cities
- controlling pollution
Here, we take a real-world problem and write it as a mathematical problem. We then follow the stages of mathematical modelling like formulation, solution, interpretation and validation. After the stages, we see to what extent the solution is valid in a real-world problem.
Example: M travels 256 kms, which takes up 16 litres of fuel. How much fuel is required to cover another 48 kilometres?
Solution: Here, we follow the stages of mathematical modelling to find out a solution.
Formulation : We get that distance travelled = 256 kms , and fuel used = 16 litres.
We now have to find out for 1 litre of fuel, what is the distance travelled.
Solution : For 1 litre of fuel used, distance covered = 256 kms / 16 = 16 kms
So, for 16 kms, fuel required = 1 litre
Then, for 1 km, fuel required = 1/16 litres.
For 48 kms, fuel required = 48 * 1/16 = 3 litres
Interpretation: If carefully seen, in this problem, we have carefully removed the facts that can be faced in the real-world like traffic jams, hilly roads / flat roads and few others. The problem is solved considering the above facts as something that will not affect the fuel or distance travelled.
Validation: After various assumptions, the solution is validated and is taken as a real-world solution only if the factors left behind during solving will not affect even in real-world scenarios.
