High School

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Roger Dist. has an annual demand of 1,650 units for metal detectors for airports. The regular cost of a detector is $445. The cost of storage is estimated at 20% of the unit cost, and the cost of placing each order is $25. If quantities of 300 or more are ordered, the cost of a detector will be $371. Roger Dist. operates for 250 business days a year, and the supplier takes 6 days to deliver a new detector order.

1. After determining the number of detectors to order at the discount price, what would be the adjusted order quantity? (If no adjustment is needed, provide the optimal order quantity.)

2. What is the total annual cost of managing the inventory if detectors are purchased at the regular price?

3. What is the total annual cost of managing the inventory if detectors are purchased at the discount price?

Answer :

Economic order quantity (EOQ) is the formula used to determine how much to order at one time. Mr. Roger should order 89 units to get the detector at the discount price.

The formula for EOQ is given by: EOQ = √2DS / H

Where: D = annual demand for the product

S = cost to place an order

H = carrying cost per unit per year

For Mr. Roger to be eligible for a discount price, he needs to order at least 300 units:

Q = 300 units At discount price, a unit of detector costs $371.

Let us now calculate the economic order quantity: EOQ = √(2 × 1650 × 25) / (0.2 × 371)= 89 units

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