Maintenance workload for the next five months $is2,500,1,500,$

$1800,2800$ 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

hour, $or$ subcontractors $at$ a cost $of$ $$18$ per hour. The initial workforce size $is10$

employees. Each employee works for $150$ regular time hours and a maximum $of60$

overtime work hours per month. Maximum capacity $of$ subcontract workers $is200$

$h$ 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.