Question

A company purchases items in bulk for getting quantity discounts in the item’s price. The price break-up is given in the table. The annual demand for the item is 5000 units. The ordering cost is Rupees 400 per order. The annual inventory carrying cost is 30 percent of the purchase price per unit. The optimal order size (in units) is .......... (Answer in integer) 

Hint:

When dealing with quantity discounts, use the EOQ formula to calculate the optimal order size for each price range. Always select the optimal order size that falls within the constraints of each price range.

Answer 1

Correct Answer: 1995

The optimal order size, or Economic Order Quantity (EOQ), is determined using the EOQ formula: EOQ = \sqrt{\frac{2DS}{H}}, where D is the annual demand, S the ordering cost, and H the holding cost per unit.

Given:
Annual demand (D) = 5000 units
Ordering cost (S) = ₹400
Annual inventory carrying cost = 30% of unit price

For each price bracket, calculate EOQ and cost:

• Price = ₹10
  Holding cost (H) = 0.3 * 10 = ₹3
  EOQ = \sqrt{\frac{2*5000*400}{3}} = \sqrt{1333333.33} ≈ 1155
• Price = ₹8
  Holding cost (H) = 0.3 * 8 = ₹2.4
  EOQ = \sqrt{\frac{2*5000*400}{2.4}} = \sqrt{1666666.67} ≈ 1291
• Price = ₹7
  Holding cost (H) = 0.3 * 7 = ₹2.1
  EOQ = \sqrt{\frac{2*5000*400}{2.1}} = \sqrt{1904761.90} ≈ 1379

The EOQ must be in the range of each price bracket for optimal cost:

• For ₹10, EOQ ≈ 1155 (fits 0 ≤ Q < 1200)
• For ₹8, EOQ ≈ 1291 (fits 1200 ≤ Q < 2000)
• For ₹7, EOQ ≈ 1379 (fits 1379 ≥ 2000)
• Since 1291 fits its price bracket and provides a lower cost than 1155 under its bracket, go with Q = 1291

Verify: The computed optimal order size 1291 falls within its respective price range of 1200 ≤ Q < 2000.

Thus, the optimal order size is 1291 units, which is within the specified range 1995,1995.