Since the process of public procurement has to be transaparent, assessment of proposals is in most cases clearly defined beforehand, strictly evaluated and it is often complicated mathematical combination of multiple factors like price and quality. This opens a room for speculation about different strategies for winning a contract, for example low price and low quality vs higher price and higher quality. This is an example of analysis of such possibilities using mathematical software Octave.
I'm keeping these notes mainly as personal notes on how to use Octave.
Alternatively it is possible to use free online tool Wolfram Alpha. For example full solution can be drawn by command
plot (x^2)/(48*y - x) from y = 1000000 to 30000000 x = 1000000 to 30000000.
sudo apt-get install octave