## Symbolic Representation

The problem can be converted into a symbolic representation as follows:

Let's denote:
- $x_1$ as the number of low quality face wash
- $x_2$ as the number of medium quality face wash
- $x_3$ as the number of high quality face wash

The objective function to maximize profits is:
\[ \text{Maximize:} \quad 3x_1 + 7x_2 + 9x_3 \]

The constraints based on the availability of rare ingredients and water are:
\[ x_1 + 3x_2 + 4x_3 \leq 100 \] (rare ingredients constraint)
\[ 4x_1 + 2x_2 + x_3 \leq 200 \] (water constraint)
\[ x_1, x_2, x_3 \geq 0 \] (non-negativity constraint)

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'low quality face wash'), ('x2', 'medium quality face wash'), ('x3', 'high quality face wash')],
    'objective_function': '3*x1 + 7*x2 + 9*x3',
    'constraints': [
        'x1 + 3*x2 + 4*x3 <= 100',
        '4*x1 + 2*x2 + x3 <= 200',
        'x1 >= 0',
        'x2 >= 0',
        'x3 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define variables
x1 = model.addVar(name="low_quality", lb=0, vtype=gp.GRB.CONTINUOUS)  # low quality face wash
x2 = model.addVar(name="medium_quality", lb=0, vtype=gp.GRB.CONTINUOUS)  # medium quality face wash
x3 = model.addVar(name="high_quality", lb=0, vtype=gp.GRB.CONTINUOUS)  # high quality face wash

# Objective function: Maximize profits
model.setObjective(3*x1 + 7*x2 + 9*x3, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 + 3*x2 + 4*x3 <= 100, name="rare_ingredients_constraint")
model.addConstr(4*x1 + 2*x2 + x3 <= 200, name="water_constraint")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Low Quality Face Wash: {x1.varValue}")
    print(f"Medium Quality Face Wash: {x2.varValue}")
    print(f"High Quality Face Wash: {x3.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("The model is infeasible or unbounded.")
```