20. A company has three plants in which it produces a standard product. It has four agencies in different parts of the country where this product is sold. The production cost varies from factory to factory and the selling price from market to market. The shipping cost per unit of the product from each market to each of the agencies is known and stable. The relevant data are given in the following table:

Determine the optimal plan so as to maximise the profits.

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(a) Plant Weekly production capacity (Units) Unit production cost (Rs) 18 1 2 3 (b) Shipping cost (in Rs) per unit: 400 300 800 To agency 24 20 1 2 3 4 1 2 5 7 3 From plant 2 3 00 m 8 4 6 2 3 4 4 5 (c) Agency Demand (Units) Selling price (Rs) 1 300 32 2 400 35 3 300 31 4 500 36