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An electronics store stocks and sells a particular brand of a personal computer. It costs the store $450 each time it places an order with the PC manufacturer. The annual cost of carrying the PCs in inventory is $170. The store manager estimates that the annual demand for the PCs will be 1200 units. Determine the optimal order quantity (answer should be correct to one decimal place).

Question

An electronics store stocks and sells a particular brand of a personal computer. It costs the store 450eachtimeitplacesanorderwiththePCmanufacturer.TheannualcostofcarryingthePCsininventoryis450 each time it places an order with the PC manufacturer. The annual cost of carrying the PCs in inventory is 170. The store manager estimates that the annual demand for the PCs will be 1200 units. Determine the optimal order quantity (answer should be correct to one decimal place).

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Solution

The optimal order quantity can be determined using the Economic Order Quantity (EOQ) model. The EOQ model minimizes the total cost of ordering and holding inventory. The formula for EOQ is:

EOQ = sqrt((2DS)/H)

where: D = Demand rate per year S = Order cost per order H = Holding cost per unit per year

Substituting the given values into the formula:

EOQ = sqrt((21200450)/170)

Now, calculate the value inside the square root:

= sqrt((1080000)/170)

= sqrt(6352.94)

EOQ = 79.7 units

Therefore, the optimal order quantity is approximately 79.7 units. However, since we cannot order a fraction of a unit, we can round this up to 80 units.

This problem has been solved

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