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GATE2020-ME-2: 47

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For a single item inventory system, the demand is continuous, which is $10000$ per year. The replenishment is instantaneous and backorders ($S$ units) per cycle are allowed as shown in the figure.

As soon as the quantity ($Q$ units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordered cost is Rs. $300$ per order. The carrying cost is Rs. $4$ per unit per year. The cost of backordering is Rs. $25$ per unit per year. Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).

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