Problem 1: Explain what the term feasibility means with respect to a mathematical programming problem.
Problem 2: Assume you are given a minimization linear programming problem that has an optimal solution. The problem is then modified by changing an equality constraint in the problem to a less-than-or-equal-to constraint. Is it possible that the modified problem is infeasible? Explain your reasoning.
Problem 3: Will changing the objective function change the feasibility of a linear programming problem? Explain your reasoning.