## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by Paul' and 'hours worked by Ringo', which we can denote as $x_1$ and $x_2$ respectively. The objective function to maximize is $8.09x_1 + 3.83x_2$. The constraints are as follows:
- $28x_1 + 8x_2 \geq 56$ (paperwork competence rating)
- $25x_1 + 29x_2 \geq 65$ (productivity rating)
- $5x_1 + 5x_2 \geq 28$ (likelihood to quit index)
- $3x_1 + 16x_2 \geq 51$ (organization score)
- $-3x_1 + 10x_2 \geq 0$ (linear combination of hours worked)
- $28x_1 + 8x_2 \leq 139$ (upper bound paperwork competence rating)
- $25x_1 + 29x_2 \leq 122$ (upper bound productivity rating)
- $5x_1 + 5x_2 \leq 147$ (upper bound likelihood to quit index)
- $3x_1 + 16x_2 \leq 205$ (upper bound organization score)
- $x_1$ is an integer (integer constraint on Paul's hours)
- $x_2$ is a continuous variable (no constraint on Ringo's hours)

## Step 2: Convert the problem into a Gurobi-compatible format
To solve this problem using Gurobi, we need to define the model, add the variables with their respective constraints, and specify the objective function.

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

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="hours_worked_by_Paul", vtype=gurobi.GRB.INTEGER)  # Integer variable for Paul
x2 = model.addVar(name="hours_worked_by_Ringo")  # Continuous variable for Ringo

# Define the objective function
model.setObjective(8.09 * x1 + 3.83 * x2, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(28 * x1 + 8 * x2 >= 56, name="paperwork_competence_rating")
model.addConstr(25 * x1 + 29 * x2 >= 65, name="productivity_rating")
model.addConstr(5 * x1 + 5 * x2 >= 28, name="likelihood_to_quit_index")
model.addConstr(3 * x1 + 16 * x2 >= 51, name="organization_score")
model.addConstr(-3 * x1 + 10 * x2 >= 0, name="linear_combination_hours_worked")
model.addConstr(28 * x1 + 8 * x2 <= 139, name="upper_bound_paperwork_competence_rating")
model.addConstr(25 * x1 + 29 * x2 <= 122, name="upper_bound_productivity_rating")
model.addConstr(5 * x1 + 5 * x2 <= 147, name="upper_bound_likelihood_to_quit_index")
model.addConstr(3 * x1 + 16 * x2 <= 205, name="upper_bound_organization_score")

# 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 Ringo: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 4: Symbolic Representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'hours worked by Paul'), ('x2', 'hours worked by Ringo')],
    'objective_function': '8.09*x1 + 3.83*x2',
    'constraints': [
        '28*x1 + 8*x2 >= 56',
        '25*x1 + 29*x2 >= 65',
        '5*x1 + 5*x2 >= 28',
        '3*x1 + 16*x2 >= 51',
        '-3*x1 + 10*x2 >= 0',
        '28*x1 + 8*x2 <= 139',
        '25*x1 + 29*x2 <= 122',
        '5*x1 + 5*x2 <= 147',
        '3*x1 + 16*x2 <= 205'
    ]
}
```