A trader bought a number of articles for Rs 1200. Ten were damaged and he sold each.of the rest at Rs 2 more than what he paid for it, thus clearinga profit of Rs 60 on the whole transaction. Find the number of articles he bought.

A manufacturer has 3 machines I, II and III installed in his factory. Machines I and II are capable of being operated for utmost 12 hours whereas machine III must be operated atleast for 5 hours a day. He produces only two items A and B each requiring the use of three machines. The number of hours required for producing 1 unit of each of the items A and B on the three machines are given below. He makes a profit of Rs 7600 on item A and Rs 400 on item B. Assume that he can sell all that he produces. (i) Formulate this as a linear programming problem. (ii) Solve the L.P.P by corner point method.

A businessman bought some items for Rs. 600. Keeping 10 items for himself he sold the remaining items at a profit of Rs. 5 per item. From the amount received in this deal he could buy 15 more items. Find the original price of each item.