GATE ME 2025 Set 1 — Question 64
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Industrial Engineering → Inventory Control → EOQ with Shortages & Discounts
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Question
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 |
Correct answer
26000 to 26100
Solution
Given:
Annual Demand () = 3000 units
Ordering Cost () = ₹ 150 per order
Carrying Cost percentage () = 40% = 0.4The Total Annual Cost () is given by:We evaluate the total cost for each price break:1. For Price (Range: ):Since 500 is outside the range , the minimum cost in this range occurs at the boundary .2. For Price (Range: ):Since 514.5 is within the range , it is a feasible .3. For Price (Range: ):Since 530.3 is less than 1000, the minimum cost in this range occurs at the lower boundary .Comparing the total costs:
The minimum total annual cost is ₹ 26050.0.
Annual Demand () = 3000 units
Ordering Cost () = ₹ 150 per order
Carrying Cost percentage () = 40% = 0.4The Total Annual Cost () is given by:We evaluate the total cost for each price break:1. For Price (Range: ):Since 500 is outside the range , the minimum cost in this range occurs at the boundary .2. For Price (Range: ):Since 514.5 is within the range , it is a feasible .3. For Price (Range: ):Since 530.3 is less than 1000, the minimum cost in this range occurs at the lower boundary .Comparing the total costs:
The minimum total annual cost is ₹ 26050.0.
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