27. A manufacturer must produce a product in sufficient quantity to meet contractual sales in the next four months. The production capacity and unit cost of production vary from month to month. The product produced in one month may be held for sale in later months, but at an estimated storage cost of Re 1 per unit per month. No storage cost is incurred for goods sold in the same month in which they are produced. There is no opening inventory and none is desired at the end of the four months. The necessary details are given in the following table:

The management wishes to know how much to produce each month in order to minimise total cost.

(a) Formulate the problem as a transportation problem by constructing the appropriate cost and requirements table.

(b) Solve the problem as formulated in (a).

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Month Contracted sales Maximum production Unit cost of production 1234 20 40 14 30 50 16 50 30 15 15 40 50 17