I have an optimization problem that has the following two constraints:
$$ \text{minimize} \, S \\ \text{Subject to:} \\ (1) \,\frac{t}{w_{0}} \le S \\ (2)A \times B \le t $$
Is it correct to divide both sides of constraint $(2)$ by $\frac{1}{w_{0}}$ like this:
$$ \frac{1}{w_{0}} \times A \times B \le \frac{t}{w_{0}} \le S \\ \Rightarrow \frac{1}{w_{0}} \times A \times B \le S $$
and delete constraint $(1)$, making the problem like this: $$ \text{minimize} \, S \\ \text{Subject to:} \\ \frac{1}{w_{0}} \times A \times B \le S $$
I actually want to delete variable $t$ from the optimization problem.