In lectures we were shown how to 'breakdown' a piece-wise linear function so that it can be used as part of a linear program.
Now, my lecturer wrote the function as $a=f(x)=\max(0,55x-11000)$ and in the program he set the following constraints: $$a\ge 0 $$ $$a \ge 55x-11000 $$ And so the objective function was: $$\text{Maximize } 121p - a $$
Before I saw his solution, I tried this: $b=g(x) = \min(0,11000-55x)$ and I made my constraints to be: $$b\le0 $$ $$b \le 11000-55x$$ And my objective was: $$\text{Maximize } 121p+b $$
So is my formulation the same?
EDIT: running simplex on both confirmed they are infact the same. I won't delete this question however, in case someone else can use it as a guide.
Yes, you are using that $-\max(f_1(x),f_2(x)) = \min(-f_1(x),-f_2(x))$ and then you use the hypograph model for $\min$ instead of the epigraph model of $\max$