23. A mineral processing company wants to decide about the number of spare gear trains it has to order out at the time of placing order, for a high horsepower gearbox connected to a grinding unit. Although the life of a gear can be as high as 30 years and more, sudden failures cannot be ruled out. In case of a failure it would be expensive and time consuming to get a spare gear train. The cost would be Rs 200,000 including the loss of production due to down time of the equipment. If ordered-out with gear box, a gear train would cost only Rs 10,000 per unit. The following data is based on an analysis of past failures ofl 00 gearboxes:

You are expected to advise the optimal order size.

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No. of spare gear trains required 0 1 2 3 4 No. of gearboxes requiring the spares 93 4 1 1