## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'packs of paper plates' and 'packs of napkins'. Let's denote 'packs of paper plates' as $x_1$ and 'packs of napkins' as $x_2$. The objective function to maximize is $2.53x_1 + 1.37x_2$. The constraints are:
1. $7x_1 + 9x_2 \geq 33$
2. $10x_1 - 10x_2 \geq 0$
3. $7x_1 + 9x_2 \leq 47$
4. $x_1$ is an integer (non-fractional)
5. $x_2$ is an integer

## Step 2: Convert the problem into a symbolic representation
The symbolic representation of the variables is:
- $x_1$ represents 'packs of paper plates'
- $x_2$ represents 'packs of napkins'

The objective function in symbolic notation is: $2.53x_1 + 1.37x_2$

The constraints in symbolic notation are:
1. $7x_1 + 9x_2 \geq 33$
2. $10x_1 - 10x_2 \geq 0$
3. $7x_1 + 9x_2 \leq 47$

## 3: Express the problem in the required JSON format
```json
{
    'sym_variables': [('x1', 'packs of paper plates'), ('x2', 'packs of napkins')], 
    'objective_function': '2.53*x1 + 1.37*x2', 
    'constraints': [
        '7*x1 + 9*x2 >= 33', 
        '10*x1 - 10*x2 >= 0', 
        '7*x1 + 9*x2 <= 47'
    ]
}
```

## 4: Implement the problem using Gurobi
To solve this problem using Gurobi, we will use Python. We need to import the Gurobi library, create a model, add variables, set the objective function, and add constraints.

```python
import gurobi as gp

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

# Define the variables
x1 = m.addVar(name="packs_of_paper_plates", vtype=gp.GRB.INTEGER)  # packs of paper plates
x2 = m.addVar(name="packs_of_napkins", vtype=gp.GRB.INTEGER)  # packs of napkins

# Set the objective function
m.setObjective(2.53 * x1 + 1.37 * x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(7 * x1 + 9 * x2 >= 33, name="sustainability_score_min")
m.addConstr(10 * x1 - 10 * x2 >= 0, name="ratio_constraint")
m.addConstr(7 * x1 + 9 * x2 <= 47, name="sustainability_score_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Packs of paper plates: {x1.varValue}")
    print(f"Packs of napkins: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```