To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote the number of treadmills as \(x_1\) and the number of stationary bikes as \(x_2\).

The symbolic representation is:
```json
{
    'sym_variables': [('x1', 'treadmills'), ('x2', 'stationary bikes')],
    'objective_function': '300*x1 + 120*x2',
    'constraints': [
        '30*x1 + 15*x2 <= 10000',  # Mover time constraint
        '50*x1 + 30*x2 <= 15000',  # Setup time constraint
        'x1 >= 0',  # Non-negativity constraint for treadmills
        'x2 >= 0'   # Non-negativity constraint for stationary bikes
    ]
}
```

This representation captures the essence of the problem: maximizing profit (`300*x1 + 120*x2`) under the constraints of limited mover time and setup time, and ensuring that the number of treadmills and stationary bikes sold is non-negative.

To solve this optimization problem using Gurobi in Python, we'll write the following code:

```python
from gurobipy import *

# Create a new model
model = Model("Fitness_Company_Profit_Optimization")

# Add variables to the model
x1 = model.addVar(vtype=GRB.INTEGER, name="treadmills")
x2 = model.addVar(vtype=GRB.INTEGER, name="stationary_bikes")

# Set the objective function
model.setObjective(300*x1 + 120*x2, GRB.MAXIMIZE)

# Add constraints
model.addConstr(30*x1 + 15*x2 <= 10000, "mover_time_constraint")
model.addConstr(50*x1 + 30*x2 <= 15000, "setup_time_constraint")

# Optimize the model
model.optimize()

# Print the solution
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Treadmills: {x1.x}")
    print(f"Stationary Bikes: {x2.x}")
    print(f"Maximum Profit: ${300*x1.x + 120*x2.x}")
else:
    print("No optimal solution found.")
```