CammIMS$162.$E$\mathrm{.}057.$

Assume you are given a minimization linear program that has an optimal solution. The problem is then modified by changing a greater$-$than$-$or$-$equal$-$to constraint in the problem to a less$-$than$-$or$-$equal$-$to constraint. Is it possible that the modified problem is infeasible? Answer yes or no and justify.

Yes, it is possible that the modified problem is infeasible. Modifying one constraint as described could cause the regions to no longer overlap.Yes, it is possible that the modified problem is infeasible. Modifying one constraint as described could cause the regions to produce alternate optimal solutions.$$ No$,$ it is not possible that the modified problem is infeasible. Modifying one constraint as described has no effect on the feasible region of the other constraints.No$,$ it is not possible that the modified problem is infeasible. Modifying one constraint as described will result in alternate optimal solutions.No$,$ it is not possible that the modified problem is infeasible. Modifying one constraint as described will result in an unbounded solution.