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A batch reactor 1x10$^{5}$ kg of a product per year. The total batch time (in hours) of the reactor is k$\sqrt{P}{_B}$, where ${P}{_B}$is the product per batch in kg and k = 1.0h/$\sqrt{k}{g}$. The operating cost of the reactor is Rs. 200/h. The total annual fixed charges are Rs. 340 x P${_B}$ and the annual raw material cost is Rs. 2x10$^{6}$. The optimum size (in kg) of each batch (adjusted to the nearest integer) is

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