## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'packs of napkins' and 'packs of paper plates', which we can denote as $x_1$ and $x_2$ respectively. The objective function to maximize is $5x_1 + 7x_2$. The constraints are as follows:
- $5.09x_1 + 4.07x_2 \geq 74$
- $21.18x_1 + 16.72x_2 \geq 87$
- $7.98x_1 + 26.08x_2 \geq 41$
- $9.28x_1 + 20.6x_2 \geq 49$
- $24.55x_1 + 10.12x_2 \geq 34$
- $10x_1 - 5x_2 \geq 0$
- $5.09x_1 + 4.07x_2 \leq 210$
- $21.18x_1 + 16.72x_2 \leq 98$
- $7.98x_1 + 26.08x_2 \leq 127$
- $9.28x_1 + 20.6x_2 \leq 199$
- $24.55x_1 + 10.12x_2 \leq 111$
- $x_1, x_2 \geq 0$ and are integers.

## Step 2: Convert the problem into a Gurobi-compatible format
We need to maximize $5x_1 + 7x_2$ subject to the given constraints. In Gurobi, this can be represented using the following Python code:

```python
import gurobi as gp

# Define the model
m = gp.Model("optimization_problem")

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

# Define the objective function
m.setObjective(5 * x1 + 7 * x2, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(5.09 * x1 + 4.07 * x2 >= 74, name="cost_constraint")
m.addConstr(21.18 * x1 + 16.72 * x2 >= 87, name="sustainability_score_constraint")
m.addConstr(7.98 * x1 + 26.08 * x2 >= 41, name="value_constraint")
m.addConstr(9.28 * x1 + 20.6 * x2 >= 49, name="weight_constraint")
m.addConstr(24.55 * x1 + 10.12 * x2 >= 34, name="portability_rating_constraint")
m.addConstr(10 * x1 - 5 * x2 >= 0, name="ratio_constraint")
m.addConstr(5.09 * x1 + 4.07 * x2 <= 210, name="budget_constraint")
m.addConstr(21.18 * x1 + 16.72 * x2 <= 98, name="max_sustainability_score_constraint")
m.addConstr(7.98 * x1 + 26.08 * x2 <= 127, name="max_value_constraint")
m.addConstr(9.28 * x1 + 20.6 * x2 <= 199, name="max_weight_constraint")
m.addConstr(24.55 * x1 + 10.12 * x2 <= 111, name="max_portability_rating_constraint")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("packs of napkins: ", x1.varValue)
    print("packs of paper plates: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 3: Provide the symbolic representation of the problem
The symbolic representation is as follows:
```json
{
    'sym_variables': [('x1', 'packs of napkins'), ('x2', 'packs of paper plates')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': [
        '5.09*x1 + 4.07*x2 >= 74',
        '21.18*x1 + 16.72*x2 >= 87',
        '7.98*x1 + 26.08*x2 >= 41',
        '9.28*x1 + 20.6*x2 >= 49',
        '24.55*x1 + 10.12*x2 >= 34',
        '10*x1 - 5*x2 >= 0',
        '5.09*x1 + 4.07*x2 <= 210',
        '21.18*x1 + 16.72*x2 <= 98',
        '7.98*x1 + 26.08*x2 <= 127',
        '9.28*x1 + 20.6*x2 <= 199',
        '24.55*x1 + 10.12*x2 <= 111',
        'x1, x2 >= 0 and are integers'
    ]
}
```

```python
import gurobi as gp

# Define the model
m = gp.Model("optimization_problem")

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

# Define the objective function
m.setObjective(5 * x1 + 7 * x2, gp.GRB.MAXIMIZE)

# Define the constraints
m.addConstr(5.09 * x1 + 4.07 * x2 >= 74, name="cost_constraint")
m.addConstr(21.18 * x1 + 16.72 * x2 >= 87, name="sustainability_score_constraint")
m.addConstr(7.98 * x1 + 26.08 * x2 >= 41, name="value_constraint")
m.addConstr(9.28 * x1 + 20.6 * x2 >= 49, name="weight_constraint")
m.addConstr(24.55 * x1 + 10.12 * x2 >= 34, name="portability_rating_constraint")
m.addConstr(10 * x1 - 5 * x2 >= 0, name="ratio_constraint")
m.addConstr(5.09 * x1 + 4.07 * x2 <= 210, name="budget_constraint")
m.addConstr(21.18 * x1 + 16.72 * x2 <= 98, name="max_sustainability_score_constraint")
m.addConstr(7.98 * x1 + 26.08 * x2 <= 127, name="max_value_constraint")
m.addConstr(9.28 * x1 + 20.6 * x2 <= 199, name="max_weight_constraint")
m.addConstr(24.55 * x1 + 10.12 * x2 <= 111, name="max_portability_rating_constraint")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("packs of napkins: ", x1.varValue)
    print("packs of paper plates: ", x2.varValue)
else:
    print("The model is infeasible")
```