Prepare an aggregate plan that uses overtime $($$$9$ per unit, maximum output $25$ units per period$)$ and inventory variation. The primary objective in this problem is to minimize backlogs to the extent possible without having any inventory remaining at the end of Period $9.$ The ending inventory in period $9$ should be zero, and the limit on backlogs is $60$ units per period. Note that Total output $=$ Total regular output $+$ Overtime quantity. Compute the total cost of your plan. Assume $20$ full$-$time workers.