A manager is applying the transportation model of linear programming to solve an aggregate planning problem. Demand in period $1$ is

$100$

units, and in period $2,$ demand is $150$ units. The manager has

$125$

hours of regular employment available for $$10/$hour each period. In addition, $50$ hours of overtime are available for $$15/$hour each period. If holding costs are $$6$ per unit each period, how many hours of overtime employment should be used in period $2?($Assume demand must be met in both periods $1$ and $2$ for the lowest possible cost and that production is $1$ unit per hour.$)$