Suppose a (continuous) linear programming problem is solved to maximize profit, and the optimal objective function value it $100. If the same problem is solved with the additional constraint that all decision variables are now integers, which of the following must be true?

the integer solution cannot be better than the continuous solution the integer and continuous solution values must be the same the integer solution can be either better or worse than the continuous solution the integer problem solution must be better than the continuous solution none of these statements are true