Beta associates produces accounting machine that have a seasonal demand pattern. We are required to plan for the optimum production rates and inventory levels for the next four quarter periods. The available production capacities during regular time and overtime, as well as other cost data are as follows:

Capacity in Units Period Regular Time Overtime Subcontract 1 1200 150 800 2 900 200 800 3 1000 350 800 4 700 350 800 Period Units of Demand 1 1200 2 1100 3 1800 4 1500 Available initial inventory = 110 Units Desired final inventory = 140 Units Regular time cost/unit = Z 100 Overtime cost/unit = Z 125 Subcontracting cost/unit = Z 145 Inventory cost/unit/period = Z 15 The cost of unused capacity = Z 40/unit

(a) Formulate the problem as a transportation model

(b) Solve the model and infer the results [This is only for assignment purpose].

AppendixLO1