To tackle 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 hours worked by Ringo,
- $x_2$ as the hours worked by Bill.

The objective function is to maximize: $3.3x_1 + 8.28x_2$

Given the constraints, we have:

1. Total combined paperwork competence rating from hours worked by Ringo and Bill $\geq 38$: $18x_1 + 3x_2 \geq 38$
2. Total combined productivity rating from hours worked by Ringo and Bill $\geq 45$: $32x_1 + 18x_2 \geq 45$
3. $9x_1 - 2x_2 \geq 0$
4. Total combined paperwork competence rating from hours worked by Ringo and Bill $\leq 62$: $18x_1 + 3x_2 \leq 62$
5. Total combined productivity rating from hours worked by Ringo and Bill $\leq 84$: $32x_1 + 18x_2 \leq 84$

The symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'hours worked by Ringo'), ('x2', 'hours worked by Bill')],
  'objective_function': '3.3*x1 + 8.28*x2',
  'constraints': [
    '18*x1 + 3*x2 >= 38',
    '32*x1 + 18*x2 >= 45',
    '9*x1 - 2*x2 >= 0',
    '18*x1 + 3*x2 <= 62',
    '32*x1 + 18*x2 <= 84'
  ]
}
```

Now, to implement this problem in Gurobi, we consider that $x_1$ can be a non-whole number (continuous variable), but $x_2$ must be an integer (integer variable). Here's how you could model and solve this problem using Python with the Gurobi library:

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Ringo")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Bill")

# Set the objective function
m.setObjective(3.3*x1 + 8.28*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(18*x1 + 3*x2 >= 38, "paperwork_competence_min")
m.addConstr(32*x1 + 18*x2 >= 45, "productivity_rating_min")
m.addConstr(9*x1 - 2*x2 >= 0, "additional_constraint")
m.addConstr(18*x1 + 3*x2 <= 62, "paperwork_competence_max")
m.addConstr(32*x1 + 18*x2 <= 84, "productivity_rating_max")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Ringo: {x1.x}")
    print(f"Hours worked by Bill: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```