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22 August, 12:04

Suppose that you are the manager of a production department that uses 1600 boxes of specific parts per year. The supplier quotes you a price of $8.50 per box for an order size of 499 boxes or less, a price of $8.00 per box for orders of 500 to 1499 boxes, and a price of $7.50 per box for an order of 1,500 or more boxes. You assign a holding cost of 25 percent of the price to this inventory. What order quantity would you use if the objective is to minimize total annual costs of holding, purchasing, and ordering? Assume ordering cost is $200/order.

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  1. 22 August, 14:33
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    1,500 or more boxes

    Explanation:

    To calculate which order quantity would minimize total cost, we will support the calculation by using the formulae of Economic Order Quantity (EOQ).

    EOQ = √2 x Demand x Ordering Cost / Holding Cost

    Order Size 499 or less

    EOQ = √2 x 1,600 x 200 / 8.5 x 25%

    EOQ = √640,000 / 2.125

    EOQ = √301,176

    EOQ = 549

    Total Cost = 1,600 / 549 x 200 + (549 / 4) x (8.5 x 25%) + 1,600 x 8.5

    Total Cost = 583 + 292 + 13,600

    Total Cost = $14,475

    Order Size 500 to 1,499

    EOQ = √2 x 1,600 x 200 / 8 x 25%

    EOQ = √640,000 / 2

    EOQ = √320,000

    EOQ = 566

    Total Cost = 1,600 / 500 x 200 + (500 / 2) x (8 x 25%) + 1,600 x 8

    Total Cost = 640 + 500 + 12,800

    Total Cost = $13,940

    Order Size 1,500 or more

    EOQ = √2 x 1,600 x 200 / 7.5 x 25%

    EOQ = √640,000 / 1.875

    EOQ = √341,333

    EOQ = 584

    Total Cost = 1,600 / 1500 x 200 + (1500 / 2) x (7.5 x 25%) + 1,600 x 7.5

    Total Cost = 213 + 1,406 + 12,000

    Total Cost = $13,619

    Hence, the total cost is minimized at the order quantity of 1,500 or more.
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