I have some question related to the Linear Programming problem:
If we have an objective function that needs to be maximized and let the feasible region be unbounded such that there is no finite optimum solution. My question is what is the meaning of "finite" here?
If we need to solve LP using the simplex method, we need to transform any constrain that is written as an inequality equation to equality equation using the addition of the slack variables, so my question is by doing this modification did we change the problem? I mean that we have added an extra variable so I think that we have created a new constraint?
Also to solve the LP using simplex method, we need to have a maximization problem, so if we have to minimize an objective function, in this case to transform it to a maximization problem all we need to do is to negate the coefficients? For example, we need to minimize $3x+y=2$; is this equivalent to maximizing $-3x-y=2$?