Inventory management question: A company experiences annual demand of 1,000 unit

Question

Inventory management question:

A company experiences annual demand of 1,000 units for an item that it purchases. The rate of demand per day is very stable, with very little variation from day to day. The item costs $50 when purchased in quantities less than 100, $48 for 100 or more. Ordering costs are $40 and the carrying cost is 25%. How much should the company buy each time an order is placed?

[Hint: Calculate EOQ and TAC at $50. Compare the TAC for 100 units at $48].

Please show the math in details

Explanation / Answer

EOQ = sqrt (2DS/H) = sqrt(2*1000*40) /(25%*50) = 80

Number of orders = 1000 / 80 = 12.5 = 13

Total cost = Cost of product + Order cost + Holding cost = 1000 * 50 + 13*40 + (80/2) * 25% * 50 = $ 51020

Order cost = # of orders * ordering cost | Holding cost = EOQ /2 * Holding cost (25%*50)

Part 2

Total cost = 1000*48 + (1000/100) * 40 + (100/2) * 25%*48 = $49000

The company should buy 100 units each time.

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