I'm currently working through some examples and questions for some basic first-order constrained optimization problems. My current issue is how "loss of generality" works in this context:
Given a problem to 'maximise' the build of a cube area by turning it into a minimisation problem and constraining it to a budget function (cost of materials etc.):
Problem 1: $\min -x(1) \ \mathsf x \ x(2) \ \mathsf x \ x(3) \\ Subject \ to \\ x(1) \ \mathsf x \ x(2) +2x(3)\ \mathsf x \ (x(1)+x(2))=b \\ x \geq 0$
The question I'm specifically struggling with is how to explain how we can set $b=1$ without loss of generality. (the other concepts of the optimization make sense to me).
Any clarification would be super helpful~
Thanks!