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 using algebraic terms.

### Symbolic Representation

Let's define:
- $x_1$ as the number of rubber gloves,
- $x_2$ as the number of bottles of ibuprofen.

The objective function is to maximize: $5x_1 + 2x_2$

Given constraints:
1. Sustainability score constraint (lower bound): $4x_1 + 2x_2 \geq 15$
2. Constraint on rubber gloves and bottles of ibuprofen: $x_1 - 5x_2 \geq 0$
3. Sustainability score constraint (upper bound): $4x_1 + 2x_2 \leq 22$
4. Integer constraints:
   - $x_1$ must be an integer.
   - $x_2$ must be an integer.

### JSON Representation

```json
{
  'sym_variables': [('x1', 'rubber gloves'), ('x2', 'bottles of ibuprofen')],
  'objective_function': '5*x1 + 2*x2',
  'constraints': [
    '4*x1 + 2*x2 >= 15',
    'x1 - 5*x2 >= 0',
    '4*x1 + 2*x2 <= 22',
    'x1 == int(x1)',
    'x2 == int(x2)'
  ]
}
```

### Gurobi Code

To implement this problem in Gurobi, we'll write the following Python code:

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(5*x1 + 2*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(4*x1 + 2*x2 >= 15, "sustainability_lower_bound")
m.addConstr(x1 - 5*x2 >= 0, "gloves_vs_bottles")
m.addConstr(4*x1 + 2*x2 <= 22, "sustainability_upper_bound")

# Optimize the model
m.optimize()

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