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A company produces three products, P₁, P₂ and P₃ from three raw materials A, B and C. One unit of product P₁ requires one unit of A, 3 units of B and 2 units of C. A unit of product P₂ requires two units each of A and B and 3 units of C, while one unit of P₃ needs 2 units of A, 6 units of B and 4 units of C. The company has a daily availability of 8 units of A, 12 units of B and 12 units of C. It is further known that the profit per unit is Rs.3, 2 and 5 for P₁, P₂ and P₃, respectively. How many units of product P₁, product P₂ and product P₃ should the company manufacture to maximize the profit? Formulate this problem as a Linear programming problem.
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