To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints in terms of these variables.

Let's denote:
- \(x_1\) as the number of bottles of ibuprofen,
- \(x_2\) as the number of cookies.

The objective function is to minimize \(7.61x_1 + 4.87x_2\).

Constraints are:
1. Portability rating constraint: \(19x_1 + 16x_2 \geq 32\)
2. Another portability rating constraint (which seems redundant but will be included for completeness): \(19x_1 + 16x_2 \geq 32\)
3. Linear constraint: \(3x_1 - x_2 \geq 0\)
4. Upper bound on total portability rating: \(19x_1 + 16x_2 \leq 95\)
5. Non-negativity and integer constraints for both variables: \(x_1, x_2 \in \mathbb{Z}^+\) (since we're limited to non-fractional numbers of items).

Thus, the symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'bottles of ibuprofen'), ('x2', 'cookies')],
    'objective_function': '7.61*x1 + 4.87*x2',
    'constraints': [
        '19*x1 + 16*x2 >= 32',
        '3*x1 - x2 >= 0',
        '19*x1 + 16*x2 <= 95',
        'x1 >= 0', 'x2 >= 0',
        'x1 == int(x1)', 'x2 == int(x2)'
    ]
}
```

Given this symbolic representation, we can now write the Gurobi code to solve the optimization problem:
```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(7.61*x1 + 4.87*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(19*x1 + 16*x2 >= 32, "portability_rating_lower_bound")
m.addConstr(3*x1 - x2 >= 0, "linear_constraint")
m.addConstr(19*x1 + 16*x2 <= 95, "portability_rating_upper_bound")

# Optimize the model
m.optimize()

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