A manager is attempting to put together an aggregate plan $($plan A$)$ 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:

Period $123456789$

Forecast $190230260280210170160260180$

The department now has $20$ full$-$time employees each of whom produces $10$ units of output per period at a cost $$6$ per unit. Beginning inventory for period $1$ is zero. Inventory carrying cost is $$5$ per unit per period, and backlog cost is $$10$ per unit per period. Assume regular monthly production is the regular capacity.

Required

a$.$ Will the current workforce be able to handle the forecast demand? Briefly explain $5$marks

b$.$ Determine the total cost of the plan $($plan A$),$ including production, inventory and backorder costs. $10$ marks

c$.$ The manager wants to determine the cost of a second $($plan B$)$ which would use subcontracting at $$8$ per unit as needed, but no more than $20$ units per period. This is meant to reduce back orders in plan A$.$ An additional constraint is that back orders cannot exceed $80$ units in any period. All other conditions are as in plan A$.$ Compute the total cost of this plan. Note that the ending inventory in period $9$ should be zero.