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 forecast.

Period	1	2	3	4	5	6	7	8	9
Forecast	190	230	260	280	210	170	160	260	180

The department now has 20 full-time employees, each of whom produces 10 units of output per period at a cost of $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.

(a) Will the current work force be able to handle the forecast demand?

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

(c) The manager wants to determine the cost of a second plan (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

(d) The manager has decided to consider a third plan (Plan C) where a decision to hire one more worker at a cost of $200 is included. Any shortfall in this plan will be made up using subcontracting at $8 per unit, with a maximum of 20 units per period. An additional constraint is that back orders cannot exceed 80 units in any period. All other conditions are as in Plan A. Note that the ending inventory in period 9 should be zero. What is the cost of this plan?

(e) Which plan should the manager implement? Why?