A manufacturer of a certain component has the following estimates of the demand for its product:

The regular production capacity for each period is 60 units while with overtime working, and additional of upto 20 units can be produced in each period. The unit cost of production in regular time is worked out to be Rs 6 whereas it would cost Rs 10 per unit for the items manufactured during overtime. You may assume that the costs would be identical in all the periods. Any production in excess of the requirement in the current period may be held at a cost of Rs 3 per unit per period. No holding cost is involved if a unit is sold in the period in which it is produced.

(a) Formulate the problem as a transportation problem; and

(b) Draw the optimal production plan for the manufacturer.

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Period : 1 2 3 4 Demand 50 50 70 85 75