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A company has an annual demand of 3000 units, the ordering cost per order is Rs. 50 and the carrying cost is Rs. 5 per unit-year. The backorder costs are estimated as Rs. 20 per unit-year. The maximum inventory is (approximately)
  • a)
    200
  • b)
    220
  • c)
    240
  • d)
    280
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A company has an annual demand of 3000 units, the ordering cost per o...
D = 3000 units
Co = Rs. 50/order
Cc = Rs. 5/unit/year
Cs = Rs. 20/unit/year
Qs =?
≃ 274
Qmax = 219.2 ≈ 220
View all questions of this test
Most Upvoted Answer
A company has an annual demand of 3000 units, the ordering cost per o...
Given information:
- Annual demand = 3000 units
- Ordering cost per order = Rs. 50
- Carrying cost per unit-year = Rs. 5
- Backorder costs per unit-year = Rs. 20

To find:
- Maximum inventory level

Explanation:
The maximum inventory level can be calculated using the Economic Order Quantity (EOQ) formula, which is given by:

EOQ = sqrt((2 * D * S) / H)

Where:
- D = annual demand (3000 units)
- S = ordering cost per order (Rs. 50)
- H = carrying cost per unit-year (Rs. 5)

Plugging in the given values, we get:

EOQ = sqrt((2 * 3000 * 50) / 5)
= sqrt(300000 / 5)
= sqrt(60000)
= 244.95 (approx.)

Since the maximum inventory level is the EOQ, which is approximately 244.95 units, we can round it up to the nearest whole number to get the maximum inventory level.

Answer:
The maximum inventory level is approximately 220 units (option B).
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