## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Paul' and 'hours worked by Dale', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $8.98x_1^2 + 6.8x_1x_2$.

## Step 3: List the constraints
The constraints given are:
- $3x_1 + 3x_2 \geq 4$ (total combined paperwork competence rating)
- $4x_1^2 + 3x_2^2 \geq 14$ (total combined organization score)
- $6x_1^2 - x_2^2 \geq 0$
- $3x_1^2 + 3x_2^2 \leq 7$ (total combined paperwork competence rating squared)
- $3x_1 + 3x_2 \leq 7$
- $4x_1 + 3x_2 \leq 18$ (total combined organization score)
- $x_1, x_2 \geq 0$ (non-negativity, implicitly assumed as hours cannot be negative)

## 4: Correct and Simplify Constraints
Correcting and simplifying the constraints based on the problem statement:
- The paperwork competence rating constraint for Paul and Dale individually is already given but not directly used in a constraint. However, their combined rating must be at least 4: $3x_1 + 3x_2 \geq 4$.
- Organization score constraint: $4x_1 + 3x_2 \leq 18$.
- Other constraints are as listed.

## 5: Formulate the problem in Gurobi
To solve this problem using Gurobi, we will use the Gurobi Python API.

## 6: Write the Gurobi Code
```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="hours_worked_by_Paul", lb=0)  # hours worked by Paul
x2 = m.addVar(name="hours_worked_by_Dale", lb=0)  # hours worked by Dale

# Define the objective function
m.setObjective(8.98 * x1**2 + 6.8 * x1 * x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(3 * x1 + 3 * x2 >= 4, name="paperwork_combined")
m.addConstr(4 * x1**2 + 3 * x2**2 >= 14, name="organization_combined_squared")
m.addConstr(6 * x1**2 - x2**2 >= 0, name="organization_vs_paperwork")
m.addConstr(3 * x1**2 + 3 * x2**2 <= 7, name="paperwork_combined_squared")
m.addConstr(3 * x1 + 3 * x2 <= 7, name="paperwork_combined_limit")
m.addConstr(4 * x1 + 3 * x2 <= 18, name="organization_combined")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Paul: ", x1.varValue)
    print("Hours worked by Dale: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 7: Symbolic Representation
```json
{
    'sym_variables': [('x1', 'hours worked by Paul'), ('x2', 'hours worked by Dale')],
    'objective_function': '8.98*x1^2 + 6.8*x1*x2',
    'constraints': [
        '3*x1 + 3*x2 >= 4',
        '4*x1^2 + 3*x2^2 >= 14',
        '6*x1^2 - x2^2 >= 0',
        '3*x1^2 + 3*x2^2 <= 7',
        '3*x1 + 3*x2 <= 7',
        '4*x1 + 3*x2 <= 18'
    ]
}
```