## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- 'x0' corresponds to 'hours worked by John'
- 'x1' corresponds to 'hours worked by Paul'
- 'x2' corresponds to 'hours worked by Bobby'
- 'x3' corresponds to 'hours worked by Dale'

## Step 2: Define the symbolic representation of the problem
The symbolic representation of the variables is:
```json
{
    'sym_variables': [
        ('x0', 'hours worked by John'), 
        ('x1', 'hours worked by Paul'), 
        ('x2', 'hours worked by Bobby'), 
        ('x3', 'hours worked by Dale')
    ],
}
```

## Step 3: Render the objective function with symbolic variables
The objective function to maximize is:
\[ 4x_0^2 + 7x_0x_1 + 4x_0x_2 + 3x_0x_3 + 6x_1x_3 + x_2x_3 + 5x_3^2 \]

## Step 4: List the constraints with symbolic variables
The constraints are:
- $x_0 \geq 0$ (Implicit, as hours cannot be negative)
- $x_1 \geq 0$ (Implicit, as hours cannot be negative)
- $x_2 \geq 0$ (Implicit, as hours cannot be negative)
- $x_3 \geq 0$ (Implicit, as hours cannot be negative)
- $8x_0 = 8$ 
- $3x_0 = 3$ 
- $1x_1 = 1$ 
- $4x_1 = 4$ 
- $6x_2 = 6$ 
- $3x_2 = 3$ 
- $8x_3 = 8$ 
- $5x_3 = 5$ 
- $3x_0 + 3x_2 \geq 8$ 
- $3x_0 + 4x_1 + 3x_2 \geq 12$ 
- $-10x_0 + 9x_2 \geq 0$ 
- $1x_1^2 + 8x_3^2 \leq 76$ 
- $6x_2^2 + 8x_3^2 \leq 64$ 
- $8x_0^2 + 6x_2^2 \leq 103$ 
- $8x_0^2 + 8x_3^2 \leq 121$ 
- $1x_1 + 6x_2 \leq 88$ 
- $8x_0 + 1x_1 + 6x_2 + 8x_3 \leq 88$ 
- $3x_0 + 4x_1 \leq 79$ 
- $3x_2 + 5x_3 \leq 39$ 
- $3x_0^2 + 3x_2^2 \leq 27$ 
- $8x_0^2 + 8x_3^2 \leq 27$ 
- $3x_0^2 + 3x_2^2 + 8x_3^2 \leq 72$ 
- $3x_0 + 4x_1 + 5x_3 \leq 20$ 
- $4x_1^2 + 3x_2^2 + 5x_3^2 \leq 73$ 
- $3x_0 + 4x_1 + 3x_2 + 5x_3 \leq 73$

## 5: Write down the complete symbolic problem representation
```json
{
    'sym_variables': [
        ('x0', 'hours worked by John'), 
        ('x1', 'hours worked by Paul'), 
        ('x2', 'hours worked by Bobby'), 
        ('x3', 'hours worked by Dale')
    ],
    'objective_function': '4*x0^2 + 7*x0*x1 + 4*x0*x2 + 3*x0*x3 + 6*x1*x3 + 1*x2*x3 + 5*x3^2',
    'constraints': [
        '8*x0 = 8',
        '3*x0 = 3',
        '1*x1 = 1',
        '4*x1 = 4',
        '6*x2 = 6',
        '3*x2 = 3',
        '8*x3 = 8',
        '5*x3 = 5',
        '3*x0 + 3*x2 >= 8',
        '3*x0 + 4*x1 + 3*x2 >= 12',
        '-10*x0 + 9*x2 >= 0',
        '1*x1^2 + 8*x3^2 <= 76',
        '6*x2^2 + 8*x3^2 <= 64',
        '8*x0^2 + 6*x2^2 <= 103',
        '8*x0^2 + 8*x3^2 <= 121',
        '1*x1 + 6*x2 <= 88',
        '8*x0 + 1*x1 + 6*x2 + 8*x3 <= 88',
        '3*x0 + 4*x1 <= 79',
        '3*x2 + 5*x3 <= 39',
        '3*x0^2 + 3*x2^2 <= 27',
        '8*x0^2 + 8*x3^2 <= 27',
        '3*x0^2 + 3*x2^2 + 8*x3^2 <= 72',
        '3*x0 + 4*x1 + 5*x3 <= 20',
        '4*x1^2 + 3*x2^2 + 5*x3^2 <= 73',
        '3*x0 + 4*x1 + 3*x2 + 5*x3 <= 73'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi as gp

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

# Define the variables
x0 = m.addVar(lb=0, name="hours_worked_by_John")
x1 = m.addVar(lb=0, name="hours_worked_by_Paul")
x2 = m.addVar(lb=0, name="hours_worked_by_Bobby")
x3 = m.addVar(lb=0, name="hours_worked_by_Dale")

# Set the fixed values
m.addConstr(x0 == 1, name="John_organization_score")
m.addConstr(3*x0 == 3, name="John_computer_competence_rating")
m.addConstr(x1 == 1, name="Paul_organization_score")
m.addConstr(4*x1 == 4, name="Paul_computer_competence_rating")
m.addConstr(6*x2 == 6, name="Bobby_organization_score")
m.addConstr(3*x2 == 3, name="Bobby_computer_competence_rating")
m.addConstr(8*x3 == 8, name="Dale_organization_score")
m.addConstr(5*x3 == 5, name="Dale_computer_competence_rating")

# Add constraints
m.addConstr(3*x0 + 3*x2 >= 8, name="combined_computer_competence_rating_John_Bobby")
m.addConstr(3*x0 + 4*x1 + 3*x2 >= 12, name="combined_computer_competence_rating_John_Paul_Bobby")
m.addConstr(-10*x0 + 9*x2 >= 0, name="hours_worked_constraint_John_Bobby")
m.addConstr(x1**2 + 8*x3**2 <= 76, name="organization_score_Paul_Dale")
m.addConstr(6*x2**2 + 8*x3**2 <= 64, name="organization_score_Bobby_Dale")
m.addConstr(8*x0**2 + 6*x2**2 <= 103, name="organization_score_John_Bobby")
m.addConstr(8*x0**2 + 8*x3**2 <= 121, name="organization_score_John_Dale")
m.addConstr(x1 + 6*x2 <= 88, name="organization_score_Paul_Bobby")
m.addConstr(8*x0 + x1 + 6*x2 + 8*x3 <= 88, name="total_organization_score")
m.addConstr(3*x0 + 4*x1 <= 79, name="combined_computer_competence_rating_John_Paul")
m.addConstr(3*x2 + 5*x3 <= 39, name="combined_computer_competence_rating_Bobby_Dale")
m.addConstr(3*x0**2 + 3*x2**2 <= 27, name="computer_competence_rating_John_Bobby")
m.addConstr(8*x0**2 + 8*x3**2 <= 27, name="computer_competence_rating_John_Dale")
m.addConstr(3*x0**2 + 3*x2**2 + 8*x3**2 <= 72, name="combined_computer_competence_rating_John_Bobby_Dale")
m.addConstr(3*x0 + 4*x1 + 5*x3 <= 20, name="combined_computer_competence_rating_John_Paul_Dale")
m.addConstr(4*x1**2 + 3*x2**2 + 5*x3**2 <= 73, name="combined_computer_competence_rating_Paul_Bobby_Dale")
m.addConstr(3*x0 + 4*x1 + 3*x2 + 5*x3 <= 73, name="total_computer_competence_rating")

# Define the objective function
m.setObjective(4*x0**2 + 7*x0*x1 + 4*x0*x2 + 3*x0*x3 + 6*x1*x3 + x2*x3 + 5*x3**2, gp.GRB.MAXIMIZE)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Hours worked by John:", x0.varValue)
    print("Hours worked by Paul:", x1.varValue)
    print("Hours worked by Bobby:", x2.varValue)
    print("Hours worked by Dale:", x3.varValue)
    print("Objective function value:", m.objVal)
else:
    print("No optimal solution found.")
```