An integer programming $($maximization$)$ problem was first solved as a linear programming problem, and the objective function value $($profit$)$ was $$253\mathrm{.}67.$ The two decision variables $($X$,$ Y$)$ in the problem had values of X $=12\mathrm{.}45$ and Y $=32\mathrm{.}75.$ If there is a single optimal solution, which of the following must be true for the optimal integer solution to this problem?