Company X has exactly two product lines and no other sources of revenue. If the consumer product line experiences a `k%` increase in revenue (where k is a positive integer) I 2015 from 2014 levels and the machine parts line experiences a `k%` decrease in revenue in 2015 from 2014 levels, did Company X's overall revenue increase or decrease in 2015?
(1) In 2014, the consumer line generated more revenue than the machine parts line.
(2) k = 8

Answer

To determine whether Company X's overall revenue increased or decreased in 2015 compared to 2014, we can analyze the situation using mathematical expressions.

### Step-by-Step Solution:

1. **Define Variables for 2014 Revenue:**
- Let \( R_c \) be the revenue from the consumer product line in 2014.
- Let \( R_m \) be the revenue from the machine parts line in 2014.

2. **Calculate Revenue Changes for 2015:**
- The consumer product line experiences a \( k\% \) increase in revenue. Thus, the revenue in 2015 becomes:
\[ R_c' = R_c + \frac{k}{100} R_c = R_c \left(1 + \frac{k}{100}\right) = R_c \left(\frac{100 + k}{100}\right) \]
- The machine parts line experiences a \( k\% \) decrease in revenue. Thus, the revenue in 2015 becomes:
\[ R_m' = R_m - \frac{k}{100} R_m = R_m \left(1 - \frac{k}{100}\right) = R_m \left(\frac{100 - k}{100}\right) \]

3. **Calculate Total Revenues for 2014 and 2015:**
- Total revenue in 2014:
\[ R_{total, 2014} = R_c + R_m \]
- Total revenue in 2015:
\[ R_{total, 2015} = R_c' + R_m' = R_c \left(\frac{100 + k}{100}\right) + R_m \left(\frac{100 - k}{100}\right) \]

4. **Determine the Change in Total Revenue:**
- To find out if the overall revenue increased or decreased, we need to compare \( R_{total, 2015} \) with \( R_{total, 2014} \):
\[ R_{total, 2015} - R_{total, 2014} = \left(R_c \left(\frac{100 + k}{100}\right) + R_m \left(\frac{100 - k}{100}\right)\right) - (R_c + R_m) \]
- Simplifying this gives:
\[ = R_c \left(\frac{100 + k}{100} - 1\right) + R_m \left(\frac{100 - k}{100} - 1\right) \]
\[ = R_c \left(\frac{k}{100}\right) + R_m \left(-\frac{k}{100}\right) \]
\[ = \frac{k}{100} (R_c - R_m) \]

5. **Analyze the Result:**
- We know from the problem statement that \( R_c > R_m \) (the consumer line generated more revenue than the machine parts line in 2014).
- Since \( k \) is a positive integer, \( \frac{k}{100} (R_c - R_m) > 0 \).
- Therefore, \( R_{total, 2015} > R_{total, 2014} \), indicating that Company X's overall revenue increased in 2015 compared to 2014.

### Conclusion:
Company X's overall revenue increased in 2015 compared to 2014.