Problem $\mathrm{A}$ Is a Two-Variable Linear Programming Problem with a Maximization Objective

True/False

Problem $\mathrm{A}$ is a two-variable linear programming problem with a maximization objective function. Problem B is a two-variable pure integer programming problem obtained from Problem A by requiring the variables to be integers and leaving all other things unchanged. If Problem A has an optimal solution with integer values for the variables, then the same solution must be optimal for Problem B as well.