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A store order bottles of shampoo throughout the year. Over time, the store has learned that the annual demand D for shampoo is constant, i.e., there is no variability. Currently, the store decides to use the optimal EOQ value Qopt every time they order a new shipment of shampoo bottles from their supplier. Assume that the annual total cost TC(Qopt) incurred by the store is $5,000.

How much does the store pay each year in holding costs (i.e., what is the annual holding cost)?

User ELVik
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Final answer:

The annual holding cost can be calculated by using the formula derived from the EOQ model. The annual holding cost is equal to the total annual cost incurred by the store. By rearranging the formula, we can calculate the annual holding cost based on the given information.

Step-by-step explanation:

The annual holding cost is the cost incurred by the store for holding inventory. It is calculated by multiplying the holding cost per unit by the average inventory level. In this case, the total annual cost incurred by the store is $5,000. To find the annual holding cost, we need to calculate the average inventory level and then multiply it by the holding cost per unit.

The Economic Order Quantity (EOQ) formula is used to calculate the optimal order quantity that minimizes the total cost of ordering and holding inventory. The formula is:

EOQ = √(2DS/H)

where:

  • D = annual demand
  • S = cost per order
  • H = holding cost per unit per year

Since the question states that the annual demand (D) is constant and there is no variability, we can assume that the EOQ value (QOPT) is equal to the annual demand (D).

Therefore, to calculate the annual holding cost, we can rearrange the EOQ formula:

Annual holding cost = (QOPT/2) * H

Given that the annual total cost (TC(QOPT)) is $5,000, we can substitute the values into the formula:

$5,000 = (QOPT/2) * H

Now, we can solve for the annual holding cost by rearranging the formula:

Annual holding cost = $5,000 * (2/QOPT)

Since the EOQ value (QOPT) is equal to the annual demand (D), we can substitute D into the formula to find the annual holding cost:

Annual holding cost = $5,000 * (2/D)

User OcuS
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