17. The Alloy Metal Company plans to purchase at least 200 quintals of scrap metal. The company decides that the scrap metal to be purchased must contain at least 100 quintals of a valuable metal M1 and no more than 35 quintals of a base metal M2. The company can purchase the scrap metal from two suppliers in unlimited quantities with the following percentages, by weight, of M1 and M2•

The price per quintal of X's scrap metal is Rs 2 and Y's scrap metal is Rs 4. The company wants to determine the quantities that it should buy from the two suppliers, so that cost is held to be minimum.

(a) Formulate the above as a linear programming problem to minimise the total cost, and

(b) Find its dual and solve it. Obtain also the optimal solution to the primal.

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Metal Supplier X Supplier Y M 25% 75% M 10% 20%