---
title: "Forecast CFL demand for next five years"
subject: "Engineering Economics"
chapter: 1
key: "semester_6/engineering_economics:forecast-cfl-demand-five-years"
source: https://www.bctengineer.com/q/semester_6/engineering_economics/forecast-cfl-demand-five-years
site: BCT Engineering
---

# Forecast CFL demand for next five years

Engineering Economics · Chapter 1: Introduction

- Asked in: 2067 Mangsir, 6 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/engineering_economics/forecast-cfl-demand-five-years
- Whole chapter: https://www.bctengineer.com/md/semester_6/engineering_economics/chapter-1

## Question

Based on the following data, forecast the demand of CFL for next five years.
| Year | 2007 | 2008 | 2009 | 2010 |
|---|---|---|---|---|
| Demand (Nos.) | 1,00,000 | 1,25,000 | 2,00,000 | 3,00,000 |

## Short answer

Using least-squares linear trend with origin mid-2008.5, Y = 181,250 + 67,500X. Forecast demand: 2011 – 350,000; 2012 – 417,500; 2013 – 485,000; 2014 – 552,500; 2015 – 620,000 nos.

## Answer

#### Method
The demand is rising steadily, so fit a straight-line trend by least squares: Y = a + bX. Take the mid-point of the years as the origin, so ΣX = 0 and
a = ΣY / n, b = ΣXY / ΣX².

Mid-year = 2008.5. Let X = (year − 2008.5), so X = −1.5, −0.5, 0.5, 1.5.

| Year | X | Y (nos.) | XY | X² |
|---|---|---|---|---|
| 2007 | −1.5 | 100,000 | −150,000 | 2.25 |
| 2008 | −0.5 | 125,000 | −62,500 | 0.25 |
| 2009 | 0.5 | 200,000 | 100,000 | 0.25 |
| 2010 | 1.5 | 300,000 | 450,000 | 2.25 |
| Total | 0 | 725,000 | 337,500 | 5.00 |

a = 725,000 / 4 = 181,250
b = 337,500 / 5 = 67,500

**Trend line: Y = 181,250 + 67,500 X**

#### Forecast
| Year | X | Demand = 181,250 + 67,500 X |
|---|---|---|
| 2011 | 2.5 | 350,000 |
| 2012 | 3.5 | 417,500 |
| 2013 | 4.5 | 485,000 |
| 2014 | 5.5 | 552,500 |
| 2015 | 6.5 | 620,000 |

**Answer: Forecast demand of CFL is 3,50,000; 4,17,500; 4,85,000; 5,52,500 and 6,20,000 nos. for 2011 to 2015.** (The straight line adds about 67,500 per year. The data are growing slightly faster than linear, so this forecast may be on the low side.)

## Check yourself

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

1. Why take X = year - 2008.5?
   A. To make demand constant
   B. Because 2008.5 is the first year
   C. To remove the trend
   D. So ΣX = 0, simplifying a = ΣY/n and b = ΣXY/ΣX^2
   Answer: D. Using the mid-point as origin cancels the sums. (Key point: Method)

2. The value of a is:
   A. 725,000 / 4 = 181,250
   B. 337,500 / 5 = 67,500
   C. 300,000
   D. 725,000 / 5
   Answer: A. a = ΣY / n. (Key point: Intercept)

3. The slope b is:
   A. 337,500 / 4
   B. ΣXY / ΣX^2 = 337,500 / 5 = 67,500
   C. 5 / 337,500
   D. 725,000 / 4
   Answer: B. Demand rises about 67,500 per year. (Key point: Slope)

4. Demand for 2011 (X = 2.5) is:
   A. 300,000
   B. 181,250 + 67,500 = 248,750
   C. 181,250 + 67,500 x 2.5 = 350,000
   D. 67,500 x 2.5 = 168,750
   Answer: C. Substitute X = 2.5. (Key point: Forecast 2011)

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