To solve this optimization problem, we first need to understand and translate the given natural language description into a symbolic representation. This involves identifying the variables, objective function, and constraints.

### Symbolic Representation:

- **Variables:**
  - \(x_1\): packs of paper plates
  - \(x_2\): packs of napkins

- **Objective Function:**
  - Maximize \(2.53x_1 + 1.37x_2\)

- **Constraints:**
  1. Sustainability score constraint (minimum): \(7x_1 + 9x_2 \geq 33\)
  2. Linear constraint: \(10x_1 - 10x_2 \geq 0\)
  3. Sustainability score constraint (maximum): \(7x_1 + 9x_2 \leq 47\)
  4. Integer constraint for packs of paper plates: \(x_1 \in \mathbb{Z}\)
  5. Integer constraint for packs of napkins: \(x_2 \in \mathbb{Z}\)

The symbolic representation in the requested format is:
```json
{
  'sym_variables': [('x1', 'packs of paper plates'), ('x2', 'packs of napkins')],
  'objective_function': 'Maximize 2.53*x1 + 1.37*x2',
  'constraints': [
    '7*x1 + 9*x2 >= 33',
    '10*x1 - 10*x2 >= 0',
    '7*x1 + 9*x2 <= 47',
    'x1 is an integer',
    'x2 is an integer'
  ]
}
```

### Gurobi Code:

To implement this optimization problem in Gurobi, we use the following Python code. This code defines the model, adds variables and constraints according to the symbolic representation, and then solves the optimization problem.

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Add variables
x1 = m.addVar(vtype=GRB.INTEGER, name="packs_of_paper_plates")
x2 = m.addVar(vtype=GRB.INTEGER, name="packs_of_napkins")

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

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

# Optimize the model
m.optimize()

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