## Problem Description and Symbolic Representation

The problem involves a fitness company that sells and installs treadmills and stationary bikes. The goal is to maximize profit given the available mover time and setup time.

### Symbolic Representation

Let's denote:
- $x_1$ as the number of treadmills
- $x_2$ as the number of stationary bikes

The objective function to maximize profit is: $300x_1 + 120x_2$

The constraints based on the available time are:
- Mover time: $30x_1 + 15x_2 \leq 10000$
- Setup time: $50x_1 + 30x_2 \leq 15000$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'treadmills'), ('x2', 'stationary bikes')],
    'objective_function': '300*x1 + 120*x2',
    'constraints': [
        '30*x1 + 15*x2 <= 10000',
        '50*x1 + 30*x2 <= 15000',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Fitness_Company_Optimization")

# Define variables
x1 = model.addVar(name="treadmills", lb=0, vtype=gp.GRB.INTEGER)  # Number of treadmills
x2 = model.addVar(name="stationary_bikes", lb=0, vtype=gp.GRB.INTEGER)  # Number of stationary bikes

# Objective function: Maximize profit
model.setObjective(300*x1 + 120*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(30*x1 + 15*x2 <= 10000, name="mover_time_constraint")  # Mover time constraint
model.addConstr(50*x1 + 30*x2 <= 15000, name="setup_time_constraint")  # Setup time constraint

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Max Profit: ${model.objVal:.2f}")
else:
    print("The model is infeasible.")
```