Final answer:
The most likely diagnosis for the patient is multiple myeloma, a type of cancer that affects plasma cells in the bone marrow.
Step-by-step explanation:
Based on the symptoms and blood work findings of a 74-year-old male patient, the most likely diagnosis is multiple myeloma.
Multiple myeloma is a type of cancer that affects plasma cells in the bone marrow. The symptoms described, including weight loss, hypercalcemia, anemia, raised white cells, and bone pain, are characteristic of multiple myeloma. The patient's smoking history and cough with red-stained sputum are additional signs of the disease.
A bone marrow biopsy and further diagnostic tests would be necessary to confirm the diagnosis.