X Ltd. is committed to supply 24,000 bearings per annum to Y Ltd. on steady basis. It is estimated that it costs 10 paise as inventory holding cost per bearing per month and that the set-up cost per run of bearing manufacture is Rs. 324. What would be the optimum run size for bearing manufacture?

Solution

To determine the optimum run size for bearing manufacture, we can use the Economic Order Quantity (EOQ) formula. The EOQ formula is given by: EOQ = √((2 * D * S) / H) Where: D = Annual demand (units) S = Set-up cost per run H = Inventory holding cost per unit per time period Given: Annual demand (D) = 24,000 bearings per annum Set-up cost per run (S) = Rs. 324 Inventory holding cost per bearing per month (H) = 10 paise = 0.10 rupees First, let's convert the holding cost to rupees per year: Holding cost per bearing per year = 0.10 rupees * 12 months = Rs. 1.20 Now, we can plug the values into the EOQ formula: EOQ = √((2 * 24,000 * 324) / 1.20) EOQ = √(15552000 / 1.20) EOQ = √12960000 EOQ ≈ 3,600 bearings (rounded off to the nearest whole number) Therefore, the optimum run size for bearing manufacture would be 3600 bearings. So, the correct option is: 3600.