Sonu gets a jewellery made of alloy of copper and silver. The alloy with a weight of 8kg contains p percent of copper. What piece of a copper-silver alloy containing 40% of silver must be alloyed with the first piece in order to obtain a new alloy with the minimum percentage of a copper if the weight of the second piece is 2Kg?

• We have two parameters to vary, percentage of copper in first piece "p" and weight of second piece which we want to take in order to minimize the percentage of copper in the resulting alloy.
  Percentage of copper in 2nd piece of alloy = 60%
  So if we p = 60%, then it doesn't matter what amount of 2nd alloy we take as the resulting percentage of copper will also be 60%. so we can take a kg where a lies in [0,2]
  If p < 60, then the more we add 2nd piece which has 60% copper, the more will be the percentage of copper in the resulting alloy. So to minimize copper % we take 0 kg of 2nd piece.
  If p > 60, then the more is the ratio of 2nd piece in the resulting alloy the minimum will be the copper % in the resulting. So we take whole available amount i.e. 2kg
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