## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation.

Let's define the variables:
- $x_1$ = tons of chocolate syrup
- $x_2$ = tons of caramel syrup

The objective is to maximize profit. Given that the profit per ton of chocolate syrup is $500 and the profit per ton of caramel syrup is $350, the objective function can be written as:

Maximize: $500x_1 + 350x_2$

The constraints based on the problem description are:
1. At most 15 tons of each syrup can be made per week: $x_1 \leq 15$, $x_2 \leq 15$
2. At least 2 tons of chocolate syrup and at least 3 tons of caramel syrup must be made per week: $x_1 \geq 2$, $x_2 \geq 3$
3. Each ton of syrup requires 3 hours on the heating machine, and the machine is available for at most 50 hours per week: $3x_1 + 3x_2 \leq 50$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'tons of chocolate syrup'), ('x2', 'tons of caramel syrup')],
    'objective_function': 'Maximize: 500*x1 + 350*x2',
    'constraints': [
        'x1 <= 15',
        'x2 <= 15',
        'x1 >= 2',
        'x2 >= 3',
        '3*x1 + 3*x2 <= 50'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(lb=2, ub=15, name="chocolate_syrup")  # tons of chocolate syrup
x2 = model.addVar(lb=3, ub=15, name="caramel_syrup")   # tons of caramel syrup

# Objective function: Maximize profit
model.setObjective(500*x1 + 350*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 <= 15, name="chocolate_syrup_limit")
model.addConstr(x2 <= 15, name="caramel_syrup_limit")
model.addConstr(x1 >= 2, name="min_chocolate_syrup")
model.addConstr(x2 >= 3, name="min_caramel_syrup")
model.addConstr(3*x1 + 3*x2 <= 50, name="heating_machine_limit")

# 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}")
else:
    print("No optimal solution found")
```