**Core Concept**
Cystic fibrosis (CF) is a genetic disorder that affects the respiratory, digestive, and reproductive systems by causing thick, sticky mucus to be produced in the lungs, pancreas, and other organs. This mucus can lead to recurrent respiratory infections, often caused by bacteria that thrive in the thick, moist environment.

**Why the Correct Answer is Right**
The greenish-colored mucus produced by the patient suggests the presence of Pseudomonas aeruginosa, a Gram-negative bacterium that is commonly associated with CF lung infections. Pseudomonas aeruginosa produces a pigment called pyocyanin, which gives the mucus a characteristic greenish color. This bacterium is known to form biofilms in the respiratory tract, making it difficult to eradicate with antibiotics. The patient's symptoms, such as fever and shortness of breath, are consistent with a Pseudomonas aeruginosa infection.

**Why Each Wrong Option is Incorrect**
**Option A:** Haemophilus influenzae is a Gram-negative coccus that can cause respiratory infections, but it is not typically associated with the greenish color of the mucus.
**Option B:** Staphylococcus aureus is a Gram-positive coccus that can cause skin and soft tissue infections, as well as respiratory infections, but it is not commonly associated with CF lung disease.
**Option C:** Klebsiella pneumoniae is a Gram-negative rod that can cause respiratory infections, but it is not typically associated with the greenish color of the mucus.

**Clinical Pearl / High-Yield Fact**
Pseudomonas aeruginosa is a common cause of lung infections in patients with cystic fibrosis, and its presence is often indicated by the production of greenish-colored mucus. This is a classic exam trap, as many students may not consider Pseudomonas aeruginosa as a primary suspect in CF lung infections.

**Correct Answer:** C.