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Example 1 A firm is engaged in producing two products, A and B. Each unit of product A requires 2kg of raw material and 4 labour hours for processing, whereas each unit of product B requires 3kg of raw material and 3 hours of labour, of the same type. Every week the firm has an availability of 60kg of raw material and 96 labour hours. One unit of product A sold yields Rs. 40, and one unit of product B sold gives Rs. 35 as profit. Formulate this problem as a linear programming problem. Use simplex method to determine how many units of each of the products should be produced per week so that the firm can earn maximum profit