GATE 2025 ME – Question 64
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).
| Order quantity | Unit price (₹) |
|---|---|
| 1 to 499 | 9.0 |
| 500 to 999 | 8.5 |
| 1000 or more | 8.0 |
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Show answer and explanation
Correct answer: 25919.75 to 26180.25
Explanation
Compute the total cost for each price. At ₹9.0 the economic order quantity is 500, which is outside the 1 to 499 range, so the best quantity is 499 and the cost is $3000 \times 9 + \frac{3000}{499}150 + 0.4 \times 9 \times \frac{499}{2} = 28800$. At ₹8.5 the economic order quantity is 514, which is in range, and the cost is $25500 + 875.5 + 873.8 = 27249$. At ₹8.0 the economic order quantity is 530, which is below the 1000 minimum, so $Q = 1000$ and the cost is $24000 + 450 + 1600 = 26050$. The minimum is ₹26050.0.