To solve the given optimization problem, we will use the Gurobi Python library. The goal is to maximize the objective function while satisfying all the constraints.

First, let's import the necessary libraries and define the variables:

We have four decision variables: hours worked by Peggy (x0), hours worked by Bobby (x1), hours worked by Bill (x2), and hours worked by George (x3).

The objective function to maximize is 7*x0 + 6*x1 + 4*x2 + 4*x3.

There are several constraints based on the computer competence rating and likelihood to quit index for each person, as well as combined constraints.

Here's how we can represent this problem in Gurobi:

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define the decision variables
x0 = m.addVar(lb=0, name="hours_worked_by_Peggy")
x1 = m.addVar(lb=0, name="hours_worked_by_Bobby")
x2 = m.addVar(lb=0, name="hours_worked_by_Bill")
x3 = m.addVar(lb=0, name="hours_worked_by_George")

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

# Add constraints based on the problem description
m.addConstr(0.56*x0 <= 222, name="Peggy_computer_rating")
m.addConstr(0.47*x0 <= 124, name="Peggy_quit_index")

m.addConstr(0.61*x1 <= 222, name="Bobby_computer_rating")
m.addConstr(0.29*x1 <= 124, name="Bobby_quit_index")

m.addConstr(0.41*x2 <= 222, name="Bill_computer_rating")
m.addConstr(1.32*x2 <= 124, name="Bill_quit_index")

m.addConstr(1.81*x3 <= 222, name="George_computer_rating")
m.addConstr(0.09*x3 <= 124, name="George_quit_index")

# Combined constraints
m.addConstr(0.56*x0 + 0.41*x2 <= 137, name="Peggy_Bill_computer_rating_combined")
m.addConstr(0.61*x1 + 1.81*x3 <= 121, name="Bobby_George_computer_rating_combined")
m.addConstr(0.56*x0 + 0.61*x1 <= 163, name="Peggy_Bobby_computer_rating_combined")
m.addConstr(0.41*x2 + 1.81*x3 <= 181, name="Bill_George_computer_rating_combined")
m.addConstr(0.56*x0 + 0.61*x1 + 0.41*x2 + 1.81*x3 <= 181, name="All_computer_rating_combined")

m.addConstr(0.29*x1 + 0.09*x3 <= 111, name="Bobby_George_quit_index_combined")
m.addConstr(0.47*x0 + 1.32*x2 <= 33, name="Peggy_Bill_quit_index_combined")
m.addConstr(0.47*x0 + 0.09*x3 <= 82, name="Peggy_George_quit_index_combined")
m.addConstr(1.32*x2 + 0.09*x3 <= 78, name="Bill_George_quit_index_combined")
m.addConstr(0.47*x0 + 0.29*x1 + 1.32*x2 + 0.09*x3 <= 78, name="All_quit_index_combined")

# Optimize the model
m.optimize()

# Print the results
for v in m.getVars():
    print(f"{v.varName}: {v.x}")

print("Objective:", m.objVal)
```