A production manager needs to develop a production schedule to meet the following demand:

Period	1	2	3	4	5	6
Demand	600	600	800	1000	1200	600

Productions costs are as follows: (a) regular time: $3 per unit. (b) over-time: $5 per unit. (c) subcontract: $7 per unit. (d) Inventory carrying cost = $2 per unit per period (e) Back-order costs = $5 per unit per period.

Suppose some workers have retired, and the regular production rate can be only 700 units per period. Further, no subcontracting is allowed. However, it is possible to schedule production on an over-time basis .