Example

Example $8\mathrm{.}10$: Maintenance workload for the next five months is $2,500,1,500,1800,2800$ and $2200$ man$-$hours. This workload can be met by employees on regular time at a cost of $$10$ per hour, employees on overtime at a cost of $$15$ per Lour, or subcontractors at a cost of $$18$ per hour. The initial workforce size is $10$ employes. Each employee works for $150$ regular time hours and a maximum of $60$ overtime work hours per month. Maximum capacity of subcontract workers is $200$ in per month. Early maintenance costs $$8$ per hour per month, while late maintenance costs $$14$ per hour per month. For each employee, hiring cost is $$800$ and firing cost is $$1000.$ Assuming zero starting and ending backlog, model and solve this capacity planning problem using mathematical programming.