Over the past year, MG has tracked the movement of employees between positions in the organization. They are interested in forecasting availabilities for four specific job positions: floor worker $($A$1),$ floor manager $($A$2),$ sales representative $($B$1)$ and sales manager $($B$2).$ At the beginning of their tracking period, MG employed $500$ floor workers, $100$ floor managers, $250$ sales representatives, and $50$ sales managers.