An electronics store stocks and sells a particular brand of personal computer. It costs the store $450 each time it places an order with the manufacturer of the PCs. 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. Calculate the total minimum inventory cost. (answer should be correct to two decimal places)

To calculate the total minimum inventory cost, we need to first find the Economic Order Quantity (EOQ), which is the number of units that a company should add to inventory with each order to minimize the total costs of inventory—such as holding costs, order costs, and shortage costs. The EOQ formula is:

EOQ = sqrt((2DS)/H)

where: D = Demand rate (annual demand) S = Setup costs (cost per order) H = Holding cost (cost per unit per year)

Substituting the given values into the formula:

EOQ = sqrt((21200450)/170) = 283.07 units (rounded to two decimal places)

The total minimum inventory cost is then calculated by adding the cost of the orders and the cost of holding the inventory. The number of orders is the annual demand divided by the EOQ, and the average inventory is EOQ/2.

Number of orders = D/EOQ = 1200/283.07 = 4.24 orders (rounded to two decimal places) Average inventory = EOQ/2 = 283.07/2 = 141.54 units (rounded to two decimal places)

Total order cost = Number of orders * cost per order = 4.24 * 450 = $1908 Total holding cost = Average inventory * holding cost per unit = 141.54 * 170 =$24061.8

Therefore, the total minimum inventory cost = Total order cost + Total holding cost = $1908 +$24061.8 = $25969.8.

To calculate the total minimum inventory cost, we need to first find the Economic Order Quantity (EOQ), which is the number of units that a company should add to inventory with each order to minimize the total costs of inventory—such as holding costs, order costs, and shortage costs.

The EOQ formula is:

EOQ = sqrt((2DS)/H)

where: D = Demand rate (annual demand) S = Setup costs (cost per order) H = Holding cost (cost per unit per year)

Substituting the given values into the formula:

EOQ = sqrt((21200450)/170) = 283.07 units (rounded to two decimal places)

The total minimum inventory cost is then calculated by adding the cost of the orders and the cost of holding the inventory. The number of orders is the annual demand divided by the EOQ, and the average inventory is EOQ/2.

Number of orders = D/EOQ = 1200/283.07 = 4.24 orders (rounded to two decimal places) Average inventory = EOQ/2 = 283.07/2 = 141.54 units (rounded to two decimal places)

Cost of orders = Number of orders * S = 4.24 * 450 = $1908 Cost of holding inventory = Average inventory * H = 141.54 * 170 =$24061.8

So, the total minimum inventory cost = Cost of orders + Cost of holding inventory = $1908 +$24061.8 = $25969.8

Therefore, the total minimum inventory cost is $25969.8.