I was given an exercise that looks as follows:
Given the following linear program:
minimize $\sum_{i=1}^{m} y_{i}x_{i}$
subject to some constraints related to $x_{i}$, prove that any extreme point of the feasible region of this linear program consists of $x_{i}$ that are some discrete numbers (0, 1 or 2 for example).
I wonder how is it possible to infer something about the extreme points mathematically without actually solving the linear program. What should the first step be when solving these type of problems?
I would like to avoid giving the exact definition of the linear program so I don't receive replies that actually solve the entire problem itself. I am just curious if there is a general approach for these type of problems?