## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Paul', 'hours worked by Jean', 'hours worked by Ringo'] which can be represented symbolically as 'x1', 'x2', and 'x3' respectively.

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- 'x1' for 'hours worked by Paul'
- 'x2' for 'hours worked by Jean'
- 'x3' for 'hours worked by Ringo'

## Step 3: Define the objective function in symbolic notation
The objective function to maximize is $7.29x_1 + 8.85x_2 + 1.49x_3$.

## 4: List the constraints in symbolic notation
The constraints are:
- $7x_1 \leq 7 \cdot 99$ (Paul's productivity rating constraint, but this seems to be an upper bound on the variable itself, not a constraint on the product of hours and rating, so it will be ignored as it doesn't make sense with the given information)
- $9x_2 \leq 9 \cdot 99$ (Jean's productivity rating constraint, similarly ignored)
- $12x_3 \leq 12 \cdot 99$ (Ringo's productivity rating constraint, similarly ignored)
- $7x_1 + 12x_3 \leq 43$
- $9x_2 + 12x_3 \leq 37$
- $7x_1 + 9x_2 + 12x_3 \leq 93$
- $x_1$ is an integer
- $x_2$ is an integer
- $x_3$ can be a real number

## 5: Correctly interpret the productivity rating constraints
Given that productivity ratings are attributes of individuals and not directly constraints on their hours worked, we focus on the constraints provided:
- The productivity ratings given are $r0 = {'x0': 7, 'x1': 9, 'x2': 12}$ for Paul, Jean, and Ringo respectively.

## 6: Formulate the optimization problem in Gurobi
We need to maximize $7.29x_1 + 8.85x_2 + 1.49x_3$ subject to:
- $7x_1 + 12x_3 \leq 43$
- $9x_2 + 12x_3 \leq 37$
- $7x_1 + 9x_2 + 12x_3 \leq 93$
- $x_1 \in \mathbb{Z}$
- $x_2 \in \mathbb{Z}$
- $x_3 \in \mathbb{R}$

## 7: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'hours worked by Paul'), ('x2', 'hours worked by Jean'), ('x3', 'hours worked by Ringo')],
    'objective_function': '7.29*x1 + 8.85*x2 + 1.49*x3',
    'constraints': [
        '7*x1 + 12*x3 <= 43',
        '9*x2 + 12*x3 <= 37',
        '7*x1 + 9*x2 + 12*x3 <= 93'
    ]
}
```

## 8: 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='hours_worked_by_Paul', vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name='hours_worked_by_Jean', vtype=gurobi.GRB.INTEGER)
    x3 = model.addVar(name='hours_worked_by_Ringo', vtype=gurobi.GRB.CONTINUOUS)

    # Define the objective function
    model.setObjective(7.29 * x1 + 8.85 * x2 + 1.49 * x3, gurobi.GRB.MAXIMIZE)

    # Add constraints
    model.addConstr(7 * x1 + 12 * x3 <= 43, name='constraint_1')
    model.addConstr(9 * x2 + 12 * x3 <= 37, name='constraint_2')
    model.addConstr(7 * x1 + 9 * x2 + 12 * x3 <= 93, name='constraint_3')

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print('Objective: ', model.objVal)
        print('Hours worked by Paul: ', x1.varValue)
        print('Hours worked by Jean: ', x2.varValue)
        print('Hours worked by Ringo: ', x3.varValue)
    else:
        print('The model is infeasible')

solve_optimization_problem()
```