---
title: "EOQ, total cost and reorder point numerical"
subject: "Industrial Engineering and Management"
chapter: 4
key: "semester_6/industrial_engineering_and_management:eoq-numerical-reorder-point"
source: https://www.bctengineer.com/q/semester_6/industrial_engineering_and_management/eoq-numerical-reorder-point
site: BCT Engineering
---

# EOQ, total cost and reorder point numerical

Industrial Engineering and Management · Chapter 4: Inventory Control

- Asked in: year not given, 6 marks
- Video: [Economic Order Quantity (EOQ) -  Problem - Material Cost - B.COM / CMA /CA INTER - By Saheb Academy](https://www.youtube.com/watch?v=xO27v9hiVAU) — Saheb Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/industrial_engineering_and_management/eoq-numerical-reorder-point
- Whole chapter: https://www.bctengineer.com/md/semester_6/industrial_engineering_and_management/chapter-4

## Question

A firm uses 12,000 units of an item per year. The unit cost is Rs 150, the ordering cost is Rs 300 per order and the carrying cost is 20% of the unit cost per year. The firm works 300 days a year and the lead time is 10 days. Find (a) the EOQ, (b) the number of orders per year and the time between orders, (c) the annual ordering plus holding cost, (d) the reorder point, and (e) the extra annual cost if the firm orders 600 units each time.

## Short answer

EOQ = 490 units; 24.5 orders/year, cycle 12.2 days; total ordering+holding cost = Rs 14,697; reorder point = 400 units; ordering 600 units increases annual cost by Rs 303.

## Answer

#### Given
$D = 12000$ units/year, $S = $ Rs 300, $H = 0.20 \times 150 = $ Rs 30 per unit per year, 300 working days, $L = 10$ days.

#### (a) EOQ

$$
Q^* = \sqrt{\frac{2DS}{H}} = \sqrt{\frac{2 \times 12000 \times 300}{30}} = \sqrt{240000} = 489.9 \approx 490\ \text{units}
$$

#### (b) Orders and cycle time

$$
N = \frac{D}{Q^*} = \frac{12000}{489.9} = 24.5\ \text{orders/year}
$$

$$
T = \frac{300}{24.5} = 12.2\ \text{working days}
$$

#### (c) Annual ordering plus holding cost
Ordering cost $= 24.49 \times 300 = $ Rs 7,348; holding cost $= (489.9/2) \times 30 = $ Rs 7,348.

$$
TC = 7348 + 7348 = \text{Rs } 14{,}697
$$

(Purchase cost is $12000 \times 150 = $ Rs 1,800,000, so the total annual cost including purchase is Rs 1,814,697.)

#### (d) Reorder point
Daily demand $d = 12000/300 = 40$ units/day.

$$
ROP = d \times L = 40 \times 10 = 400\ \text{units}
$$

An order of 490 units is placed when the stock falls to 400 units.

#### (e) Order quantity of 600

$$
TC_{600} = \frac{12000}{600}(300) + \frac{600}{2}(30) = 6000 + 9000 = \text{Rs } 15{,}000
$$

Extra cost $= 15000 - 14697 = $ Rs 303 per year (about 2.1% higher).

**Answer: EOQ = 490 units; 24.5 orders/year, every 12.2 working days; TC = Rs 14,697; ROP = 400 units; ordering 600 costs Rs 303 more per year.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is H in this problem?
   A. Rs 150
   B. Rs 300
   C. Rs 3
   D. Rs 30
   Answer: D. H = 0.20 x 150 = Rs 30 per unit per year. (Key point: Holding cost)

2. What is the EOQ?
   A. About 490 units
   B. About 600 units
   C. About 240 units
   D. About 400 units
   Answer: A. sqrt(2 x 12000 x 300 / 30) = sqrt(240000) = 489.9. (Key point: EOQ value)

3. How is the reorder point calculated?
   A. EOQ x lead time
   B. Daily demand x lead time = 40 x 10 = 400 units
   C. Annual demand / EOQ
   D. EOQ / 2
   Answer: B. Daily demand is 12000/300 = 40, times 10 days. (Key point: Reorder point)

4. What is the extra annual cost if 600 units are ordered each time?
   A. Rs 15,000
   B. Rs 14,697
   C. Rs 303
   D. Rs 0
   Answer: C. TC at 600 is 6000 + 9000 = Rs 15,000, which is Rs 303 above Rs 14,697. (Key point: Order of 600)

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