Problem $11-12($Static$)$

A manager is attempting to put together an aggregate plan for the coming nine months. She has obtained a forecast of expected demand for the planning horizon. The plan must deal with highly seasonal demand; demand is relatively high in periods $3$ and $4$ and again in period $8,$ as can be seen from the following forecasts:

The department now has $20$ full$-$time employees, each of whom can produce $10$ units of output per period at a cost of $\backslash (\backslash$$ $6\backslash )$ per unit. Inventory carrying cost is $\backslash (\backslash$$ $5\backslash )$ per unit per period, and backlog cost is $\backslash (\backslash$$ $10\backslash )$ per unit per period.

Prepare an aggregate plan that uses overtime $(\backslash (\backslash$$ $9\backslash )$ 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.

Total cost