## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Laura', 'hours worked by Peggy', and 'hours worked by Dale', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $1x_0^2 + 6x_1^2 + 3x_2^2 + 8x_1$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $3x_0 \leq 25$ (computer competence rating for Laura, but it's given as a fixed value, so $x_0$ is not directly constrained by this but by its attribute)
- $8x_0 \leq 67$ (organization score for Laura)
- $5x_1 \leq 25$ (computer competence rating for Peggy)
- $7x_1 \leq 67$ (organization score for Peggy)
- $1x_2 \leq 25$ (computer competence rating for Dale)
- $1x_2 \leq 67$ (organization score for Dale)
- $x_0^2 + x_1^2 + x_2^2 \geq 18$ (total combined organization score squared)
- $-10x_0 + 3x_2 \geq 0$ (relationship between hours worked by Laura and Dale)
- $5x_1 + 1x_2 \leq 23$ (total combined computer competence rating from Peggy and Dale)
- $3x_0 + 5x_1 \leq 24$ (total combined computer competence rating from Laura and Peggy)
- $3x_0 + 5x_1 + 1x_2 \leq 24$ (total combined computer competence rating from all)
- $8x_0 + 1x_2 \leq 23$ (total combined organization score from Laura and Dale)
- $7x_1 + 1x_2 \leq 23$ (total combined organization score from Peggy and Dale)
- $8x_0 + 7x_1 + 1x_2 \leq 59$ (total combined organization score from all)
- $x_2$ is an integer (hours worked by Dale)

## 4: Correct and Simplify Constraints Based on Given Attributes
Given attributes:
- $r0$: computer competence rating, with $x_0 = 3$, $x_1 = 5$, $x_2 = 1$
- $r1$: organization score, with $x_0 = 8$, $x_1 = 7$, $x_2 = 1$

These imply direct values rather than constraints for $x_0$, $x_1$, and $x_2$ based on their ratings.

## 5: Formulate the Symbolic Representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x0', 'hours worked by Laura'), ('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Dale')],
'objective_function': '1*x0^2 + 6*x1^2 + 3*x2^2 + 8*x1',
'constraints': [
    'x0^2 + x1^2 + x2^2 >= 18',
    '-10*x0 + 3*x2 >= 0',
    '5*x1 + x2 <= 23',
    '3*x0 + 5*x1 <= 24',
    '3*x0 + 5*x1 + x2 <= 24',
    '8*x0 + x2 <= 23',
    '7*x1 + x2 <= 23',
    '8*x0 + 7*x1 + x2 <= 59'
]
}
```

## 6: Implement the Optimization Problem using Gurobi
```python
import gurobi

def optimize_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="x0", lb=0)  # hours worked by Laura
    x1 = model.addVar(name="x1", lb=0)  # hours worked by Peggy
    x2 = model.addVar(name="x2", lb=0, type=gurobi.GRB.INTEGER)  # hours worked by Dale

    # Objective function
    model.setObjective(1 * x0**2 + 6 * x1**2 + 3 * x2**2 + 8 * x1, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x0**2 + x1**2 + x2**2 >= 18)
    model.addConstr(-10 * x0 + 3 * x2 >= 0)
    model.addConstr(5 * x1 + x2 <= 23)
    model.addConstr(3 * x0 + 5 * x1 <= 24)
    model.addConstr(3 * x0 + 5 * x1 + x2 <= 24)
    model.addConstr(8 * x0 + x2 <= 23)
    model.addConstr(7 * x1 + x2 <= 23)
    model.addConstr(8 * x0 + 7 * x1 + x2 <= 59)

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Laura: ", x0.varValue)
        print("Hours worked by Peggy: ", x1.varValue)
        print("Hours worked by Dale: ", x2.varValue)
    else:
        print("The model is infeasible")

optimize_problem()
```