A company uses 3000 units of a part annually. The units are priced as given in the table below. It costs ₹150 to place an order. Carrying costs are 40 percent of the purchase price per unit on an annual basis. The minimum total annual cost is ₹ _________ (rounded off to 1 decimal place).
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To minimize total annual costs, calculate the Economic Order Quantity (EOQ) and compare the total annual costs for different order quantities. The price per unit and the carrying costs play a significant role.
Step 1: Understanding the given values.
Annual demand: 3000 units
Ordering cost: ₹150 per order
Carrying cost rate: 40% of the unit price per year
The company has three price categories based on order quantity. We need to determine which order quantity minimizes the total annual cost.
Step 2: Calculating the Economic Order Quantity (EOQ).
The EOQ formula is given by:
\[
EOQ = \sqrt{\frac{2DS}{H}}
\]
where:
\( D \) is the annual demand (3000 units),
\( S \) is the ordering cost (₹150),
\( H \) is the holding cost per unit per year.
The holding cost \( H \) is 40% of the unit price.
Step 3: Total annual cost calculation for each price category.
For each price category, calculate the total annual cost, which includes the ordering cost, holding cost, and the cost of purchasing the units:
\[
\text{Total Annual Cost} = \text{Ordering Cost} + \text{Holding Cost} + \text{Purchase Cost}
\]
After calculating the total annual costs for each price range, the minimum cost comes out to be ₹26,000.00 when the order quantity is in the range of 1000 or more units.
