Question:hard

The demand for a commodity is 100 units per day. Every time an order is placed, a fixed cost of Rs 400 is incurred and the holding cost is Rs 0.08 per unit per day. If the lead time is 13 days, then the economic lot size and the reorder point are in units

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Always ensure your time units are fully uniform! Here, demand is units/day and holding cost is Rs/unit/day. Because they match, you do not need to convert them into annual figures. For ROP, remember: if Lead Time Demand > $Q$, subtract $Q$ repeatedly until the value is less than $Q$. \[ 1300 - 1000 = 300 \]
Updated On: Jul 4, 2026
  • 800 and 130
  • 840 and 100
  • 890 and 300
  • 1000 and 300
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Find the economic order quantity using the EOQ formula.
With demand \( D = 100 \) units/day, ordering cost \( C_o = Rs.\,400 \) per order and holding cost \( C_h = Rs.\,0.08 \) per unit per day, the economic lot size is \[ Q^* = \sqrt{\frac{2DC_o}{C_h}} = \sqrt{\frac{2 \times 100 \times 400}{0.08}} = \sqrt{1{,}000{,}000} = 1000 \text{ units} \]

Step 2: Work out how long one order cycle lasts.
An order of 1000 units at a consumption rate of 100 units per day lasts \[ t_c = \frac{Q^*}{D} = \frac{1000}{100} = 10 \text{ days} \] so a fresh batch of 1000 units is consumed in exactly 10 days.

Step 3: Locate the reorder point within the lead time.
The lead time is 13 days, which is one full 10 day cycle plus 3 extra days. So when the order is placed, stock only needs to cover those leftover 3 days of demand before the fresh batch lands, giving \[ \text{ROP} = 3 \times 100 = \boxed{300 \text{ units}} \] Together with \( Q^* = 1000 \) units, this matches option 4.
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