In the case of $$lower hiring and layoff costs$($case $3),$ the optimal solution recommends $20$ units of subcontracting for period $6($the solver solution for case $3),$ with an optimal cost of $$412,770.$

For this situation what happens if you don$$t follow the recommended optimal solution but instead of subcontracting, you hire one extra person for the last period? Why will the total cost due to hiring one extra person be higher than the optimal cost with subcontracting?