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The problem asks for the number of lighting fixtures needed in an office space using the lumen method. Let's break it down step by step:

### Given Data:
1. **Room dimensions**: 15 m x 20 m
   - Area \( A = 15 \, \text{m} \times 20 \, \text{m} = 300 \, \text{m}^2 \)
2. **Illumination requirement**: 320 lux (lumen per square meter)
3. **Utilization factor (UF)**: 0.6
4. **Maintenance factor (MF)**: 0.8
5. **Lamp efficiency**: 60 lumens per watt
6. **Lamp wattage**: 40 W per tube

### Step 1: Total Luminous Flux Required
The luminous flux (\( \Phi \)) required for the space is calculated by multiplying the area by the required illumination:

\[
\Phi = \text{Illumination Requirement} \times \text{Area} = 320 \, \text{lux} \times 300 \, \text{m}^2 = 96,000 \, \text{lumens}
\]

### Step 2: Effective Luminous Flux from Each Fixture
The actual luminous output of each lamp takes into account the utilization and maintenance factors. First, calculate the luminous flux produced by one tube:

\[
\text{Luminous Flux per tube} = 60 \, \text{lumens/watt} \times 40 \, \text{W} = 2400 \, \text{lumens}
\]

Now, apply the utilization and maintenance factors:

\[
\text{Effective Luminous Flux per tube} = 2400 \, \text{lumens} \times 0.6 \times 0.8 = 1152 \, \text{lumens}
\]

### Step 3: Number of Fixtures Needed
Now, determine how many lighting fixtures are required to meet the total luminous flux requirement:

\[
\text{Number of fixtures} = \frac{\text{Total Luminous Flux Required}}{\text{Effective Luminous Flux per tube}} = \frac{96,000 \, \text{lumens}}{1152 \, \text{lumens/tube}} \approx 83.33
\]

Since the number of fixtures must be a whole number, you will need **84 lighting fixtures**.

Would you like a detailed illustration on the ceiling layout, or have any questions about the method?

Here are five follow-up questions:
1. What is the role of the maintenance factor in lighting design?
2. How would the required number of fixtures change if the room's area increased?
3. What happens if the utilization factor decreases?
4. How do different lamp efficiencies affect the number of fixtures needed?
5. Can the same method be used for other types of lighting (e.g., LED)?

**Tip:** Always account for both the utilization and maintenance factors to get an accurate estimate of how many fixtures you'll need.

COMPUTE IN LUMEN METHOD: An office space has a 15m x 20m room dimension. It has a utilization factor of 0.6 and a maintenance factor of 0.8. Taking also the lamp efficiency 60 lumens/watt for a 40W tube, how many lighting fixtures are needed so that it will reach the 320 lux illumination requirement? Draw and illustrate how you will apply this number to a ceiling layout. (Drawings and sketches do not need to be scaled).

Learn how to compute the number of lighting fixtures needed for a 15m x 20m office space using the lumen method. This problem involves calculating total luminous flux, lamp efficiency, and applying factors such as utilization and maintenance. Perfect for college-level students studying lighting design or energy efficiency.

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