---
title: "Break-even units and output for desired profit"
subject: "Engineering Economics"
chapter: 1
key: "semester_6/engineering_economics:breakeven-units-profit-50000"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/breakeven-units-profit-50000
site: BCT Engineering
---

# Break-even units and output for desired profit

Engineering Economics · Chapter 1: Introduction

- Asked in: 2072 Asoj, 4 marks
- Video: ["Break - Even Point" Formulas & Problems](https://www.youtube.com/watch?v=Idum--hF73s) — Devika's Commerce & Management Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/breakeven-units-profit-50000
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-1

## Question

A company produces an electronics timing switch that is used in consumer and commercial products made by several other manufacturing firms. The fixed cost and total cost are Rs. 40,000 and Rs. 85,000 respectively. The total sales are Rs. 1,05,000 and sales volume is 15,000 for this situation.
i) Find the breakeven points in terms of number of units.
ii) What should be the output if the profit desired is Rs. 50,000?

## Short answer

Fixed cost Rs 40,000. Variable cost per unit = (85,000−40,000)/15,000 = Rs 3, price = 105,000/15,000 = Rs 7. Break-even quantity = 40,000/(7−3) = 10,000 units. For desired profit Rs 50,000, output = (40,000+50,000)/4 = 22,500 units.

## Answer

#### Data
- Fixed cost FC = Rs 40,000; total cost TC = Rs 85,000 at 15,000 units
- Sales = Rs 105,000 at 15,000 units

#### Unit values
- Total variable cost = 85,000 − 40,000 = Rs 45,000, so v = 45,000 / 15,000 = **Rs 3 per unit**
- Selling price p = 105,000 / 15,000 = **Rs 7 per unit**
- Contribution per unit = p − v = 7 − 3 = Rs 4

#### (i) Break-even point
Q* = FC / (p − v) = 40,000 / 4 = **10,000 units**
(Break-even sales = 10,000 × 7 = Rs 70,000.)

#### (ii) Output for a desired profit of Rs 50,000
Revenue − cost = profit: 7Q − (40,000 + 3Q) = 50,000
Q = (40,000 + 50,000) / 4 = **22,500 units**

Check: 22,500 × 7 = 157,500; cost = 40,000 + 67,500 = 107,500; profit = 50,000.

**Answer: BEP = 10,000 units; output for Rs 50,000 profit = 22,500 units.** (The desired output exceeds the 15,000 units now sold, so sales must grow by 7,500 units.)

## Check yourself

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

1. How is v found from the data?
   A. (Total cost - fixed cost) / units = 45,000/15,000 = Rs 3
   B. Total cost / units = Rs 5.67
   C. Sales / units = Rs 7
   D. Fixed cost / units = Rs 2.67
   Answer: A. Variable cost = 85,000 - 40,000 = 45,000, over 15,000 units gives Rs 3. (Key point: Variable cost per unit)

2. The break-even point is:
   A. 15,000 units
   B. 10,000 units
   C. 22,500 units
   D. 5,714 units
   Answer: B. Q* = 40,000 / (7 - 3) = 10,000. (Key point: Break-even units)

3. Units needed for Rs 50,000 profit:
   A. (FC - profit)/4 = -2,500 units
   B. 50,000/4 = 12,500 units
   C. (FC + profit)/(p - v) = 22,500 units
   D. 10,000 + 50,000 units
   Answer: C. Contribution must cover fixed cost plus profit: 90,000/4 = 22,500. (Key point: Output for target profit)

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