a) A company purchasing scrap material has two types of scarp materials available. The first type has 30% of material X, 20% of material Y and 50% of material Z by weight. The second type has 40% of material X, 10% of material Y and 30% of material Z. The costs of the two scraps are Rs.120 and Rs.160 per kg respectively. The company requires at least 240 kg of material X, at most 100 kg of material Y and exactly 290 kg of material Z. The company wants to determine the optimum quantities of the two scraps to be purchased so that their requirements of the three materials are satisfied at a minimum cost. Formulate the problem as a linear programming problem.

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