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Determine the economic lot size, the number of production runs per year and the total inventory costs.

A manufacturing company uses an EOQ (Economic Order Quantity) approach in planning its production of gears. The following information is available. Each gear costs Rs. 250 per unit, annual demand is 60,000 gears, set up costs are Rs. 4,000 per setup and the inventory carrying cost per month is established at 2% of the average inventory value. When in production, these gears can be produced at the rate of 400 units per day and this company works only for 300 days a year. Determine the economic lot size, the number of production runs per year and the total inventory costs. -

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$\text{Demand D = 60000 per year} \\ \text{Cost price Cp = Rs. 250 per unit} \\ \text{Set up costs Co = Rs. 4000 per setup} \\ \text{Inventory carrying costs Ch = 2% per month = 24% per year} \\ \text{Production capacity P = 400 × 300 = 120000 per year}$

Economic Lot Size:

$Q*$ $= \sqrt{\bigg(\dfrac{2.D.Co}{Ch}\bigg)} × \sqrt{\bigg(\dfrac{P}{P-D}\bigg)} \\ = \sqrt{\bigg(\dfrac{2.D.Co}{Cp.I} \bigg)}× \sqrt{(\dfrac{P}{P-D})} \\ = \sqrt{\bigg(\dfrac{2×60000×4000}{250×0.24} \bigg)}× \sqrt{\bigg(\dfrac{120000}{120000-60000}\bigg)} \\ = 4000 \ units$

Number of production runs per year: N = 60000/4000 = 15 runs

$\text{Total inventory costs}$ $= \text{Holding costs + setup costs} = \dfrac{Q.Ch}{2} ×\bigg(1-\dfrac DP\bigg) +N×Co \\ = \dfrac{4000×250×0.24}{2} ×\bigg(1-\dfrac{60000}{120000}\bigg) + 15×4000 = Rs. 120000$

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