## Step 1: Define the symbolic representation of the variables
The variables are 'paper towel rolls' and 'lightbulbs', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $9.45x_1 + 4.16x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $19x_1 + 28x_2 \geq 93$
2. $9x_1 - 7x_2 \geq 0$
3. $19x_1 + 28x_2 \leq 114$
4. $x_1$ is an integer
5. $x_2$ is an integer

## 4: Consider the bounds of the resources
Given that $x_0$ and $x_1$ are the values for 'paper towel rolls' and 'lightbulbs' with an upper bound for the total value $r_0$ of 219, we have:
- The value of 'paper towel rolls' is $19x_1$.
- The value of 'lightbulbs' is $28x_2$.
- The total value $r_0 = 19x_1 + 28x_2$ has an upper bound of 219.

## 5: Compile the symbolic representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x1', 'paper towel rolls'), ('x2', 'lightbulbs')],
'objective_function': '9.45*x1 + 4.16*x2',
'constraints': [
    '19*x1 + 28*x2 >= 93',
    '9*x1 - 7*x2 >= 0',
    '19*x1 + 28*x2 <= 114',
    'x1 is an integer',
    'x2 is an integer'
]
}
```

## 6: Write the Gurobi code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name='paper_towel_rolls', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='lightbulbs', vtype=gurobi.GRB.INTEGER)

    # Define the objective function
    model.setObjective(9.45 * x1 + 4.16 * x2, gurobi.GRB.MINIMIZE)

    # Define the constraints
    model.addConstr(19 * x1 + 28 * x2 >= 93)
    model.addConstr(9 * x1 - 7 * x2 >= 0)
    model.addConstr(19 * x1 + 28 * x2 <= 114)

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print('Optimal solution found.')
        print(f'Paper towel rolls: {x1.varValue}')
        print(f'Lightbulbs: {x2.varValue}')
        print(f'Objective function value: {model.objVal}')
    else:
        print('No optimal solution found.')

solve_optimization_problem()
```