To solve this optimization problem, we first need to understand the objective function and the constraints provided. The objective function is a quadratic function of the hours worked by Jean, Peggy, George, and Mary. The constraints include bounds on various linear and quadratic combinations of these hours worked, reflecting productivity ratings, likelihood to quit indices, computer competence ratings, and organization scores.

Given the complexity and the number of constraints, directly writing down the Gurobi code requires careful consideration of how to represent each constraint and the objective function accurately.

### Step 1: Define the Model and Variables

We start by importing the necessary libraries and defining the model and variables.

### Step 2: Define the Objective Function

The objective function to minimize is given as:
\[ 6.0J^2 + 6.79JP + 7.63JG + 5.35JM + 3.06P^2 + 2.94PG + 3.06PM + 8.23G^2 + 8.03GM + 4.6M^2 + 5.47J + 6.14P + 1.27G + 8.79M \]

### Step 3: Define the Constraints

There are numerous constraints provided, including:

1. Individual productivity, likelihood to quit, computer competence, and organization scores.
2. Various combined productivity, likelihood to quit, computer competence, and organization score constraints.

### Implementation

Here is the Gurobi code for the problem:

```python
import gurobi as gp

# Define the model
m = gp.Model("optimization_problem")

# Define the variables
J = m.addVar(name="hours_worked_by_Jean", lb=0)
P = m.addVar(name="hours_worked_by_Peggy", lb=0)
G = m.addVar(name="hours_worked_by_George", lb=0)
M = m.addVar(name="hours_worked_by_Mary", lb=0)

# Define the objective function
m.setObjective(6.0*J**2 + 6.79*J*P + 7.63*J*G + 5.35*J*M + 
               3.06*P**2 + 2.94*P*G + 3.06*P*M + 
               8.23*G**2 + 8.03*G*M + 4.6*M**2 + 
               5.47*J + 6.14*P + 1.27*G + 8.79*M, gp.GRB.MINIMIZE)

# Individual attribute constraints
m.addConstraint(J >= 0)
m.addConstraint(P >= 0)
m.addConstraint(G >= 0)
m.addConstraint(M >= 0)

# Productivity rating constraints
productivity_ratings = {
    'Jean': 0.11,
    'Peggy': 0.15,
    'George': 0.24,
    'Mary': 0.69,
}

# Likelihood to quit index constraints
likelihood_to_quit_indices = {
    'Jean': 0.25,
    'Peggy': 0.79,
    'George': 0.72,
    'Mary': 0.27,
}

# Computer competence rating constraints
computer_competence_ratings = {
    'Jean': 0.85,
    'Peggy': 0.07,
    'George': 0.26,
    'Mary': 0.25,
}

# Organization score constraints
organization_scores = {
    'Jean': 0.69,
    'Peggy': 0.03,
    'George': 0.6,
    'Mary': 0.18,
}

# Combined productivity rating constraints
m.addConstraint(0.15*P**2 + 0.69*M**2 >= 59)
m.addConstraint(0.15*P + 0.24*G >= 67)
m.addConstraint(0.11*J + 0.69*M >= 34)
m.addConstraint(0.11*J**2 + 0.24*G**2 >= 45)
m.addConstraint(0.24*G**2 + 0.25*M**2 >= 38)
m.addConstraint(0.11*J + 0.15*P + 0.69*M >= 63)
m.addConstraint(0.15*P + 0.24*G + 0.25*M >= 63)
m.addConstraint(0.11*J + 0.24*G + 0.69*M >= 63)
m.addConstraint(0.11*J**2 + 0.15*P**2 + 0.24*G**2 >= 63)
m.addConstraint(0.11*J**2 + 0.15*P**2 + 0.25*M**2 >= 47)
m.addConstraint(0.15*P + 0.24*G + 0.25*M >= 47)
m.addConstraint(0.11*J + 0.24*G + 0.69*M >= 47)
m.addConstraint(0.11*J**2 + 0.15*P**2 + 0.24*G**2 >= 47)
m.addConstraint(0.11*J + 0.15*P + 0.69*M >= 38)
m.addConstraint(0.15*P + 0.24*G + 0.25*M >= 38)
m.addConstraint(0.11*J + 0.24*G + 0.69*M >= 38)
m.addConstraint(0.11*J**2 + 0.15*P**2 + 0.24*G**2 >= 38)

# Likelihood to quit index constraints
m.addConstraint(0.25*J**2 + 0.79*P**2 >= 36)
m.addConstraint(0.25*J**2 + 0.79*P**2 + 0.72*G**2 >= 59)
m.addConstraint(0.25*J + 0.79*P + 0.72*G + 0.27*M >= 59)

# Computer competence rating constraints
m.addConstraint(0.26*G + 0.25*M >= 67)
m.addConstraint(0.85*J**2 + 0.25*M**2 >= 74)
m.addConstraint(0.85*J + 0.07*P >= 76)
m.addConstraint(0.85*J + 0.26*G >= 71)
m.addConstraint(0.07*P + 0.26*G >= 44)
m.addConstraint(0.07*P + 0.26*G + 0.25*M >= 75)
m.addConstraint(0.85*J + 0.07*P + 0.26*G >= 75)
m.addConstraint(0.07*P + 0.26*G + 0.25*M >= 76)
m.addConstraint(0.85*J**2 + 0.07*P**2 + 0.26*G**2 >= 76)

# Organization score constraints
m.addConstraint(0.69*J + 0.18*M >= 24)
m.addConstraint(0.6*G**2 + 0.18*M**2 >= 20)
m.addConstraint(0.69*J + 0.6*G >= 45)
m.addConstraint(0.03*P**2 + 0.18*M**2 >= 21)
m.addConstraint(0.69*J + 0.03*P >= 25)
m.addConstraint(0.69*J + 0.03*P + 0.6*G >= 41)
m.addConstraint(0.69*J + 0.6*G + 0.18*M >= 41)

# Other constraints
m.addConstraint(9*P - 8*M >= 0)
m.addConstraint(-8*G + 3*M >= 0)
m.addConstraint(0.79*P**2 + 0.27*M**2 <= 162)
m.addConstraint(0.25*J + 0.79*P + 0.27*M <= 106)
m.addConstraint(0.85*J + 0.07*P + 0.25*M <= 169)
m.addConstraint(0.85*J**2 + 0.07*P**2 + 0.26*G**2 <= 308)
m.addConstraint(0.07*P + 0.26*G + 0.25*M <= 208)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.Status.OPTIMAL:
    print("Optimal Solution:")
    print(f"Hours worked by Jean: {J.varValue}")
    print(f"Hours worked by Peggy: {P.varValue}")
    print(f"Hours worked by George: {G.varValue}")
    print(f"Hours worked by Mary: {M.varValue}")
else:
    print("No optimal solution found.")
```