To solve this optimization problem, we will use the Gurobi Python API. The problem can be formulated as a linear programming problem with three decision variables: hours worked by Bobby (x0), hours worked by Paul (x1), and hours worked by George (x2).

The objective function is to minimize 7.06*x0 + 2.87*x1 + 5.24*x2.

There are several constraints:

- The total combined work quality rating from hours worked by Bobby plus hours worked by Paul should be at least 61.
- The total combined work quality rating from hours worked by Bobby plus hours worked by Paul plus hours worked by George should be at least 61.
- The total combined likelihood to quit index from hours worked by Paul plus hours worked by George must be at least 49.
- The total combined likelihood to quit index from hours worked by Bobby plus hours worked by Paul should be at least 25.
- The total combined likelihood to quit index from hours worked by Bobby plus hours worked by Paul plus hours worked by George has to be at least 25.
- The total combined paperwork competence rating from hours worked by Bobby plus hours worked by Paul should be at least 39.
- The total combined paperwork competence rating from hours worked by Paul plus hours worked by George must be at least 64.
- The total combined paperwork competence rating from hours worked by Bobby and hours worked by George should be at least 56.
- The total combined paperwork competence rating from hours worked by Bobby, hours worked by Paul, and hours worked by George must be at least 56.
- The total combined likelihood to quit index from hours worked by Bobby plus hours worked by Paul should be no more than 87.
- The total combined likelihood to quit index from hours worked by Paul and hours worked by George has to be less than or equal to 97.

We also have constraints on the individual work quality ratings, likelihood to quit indices, and paperwork competence ratings for each person.

Here is the Gurobi code that captures this problem:

```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_Bobby")
x1 = m.addVar(lb=0, name="hours_worked_by_Paul")
x2 = m.addVar(vtype=GRB.INTEGER, lb=0, name="hours_worked_by_George")

# Define the objective function
m.setObjective(7.06*x0 + 2.87*x1 + 5.24*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(18.72*x0 + 11.73*x1 >= 61, name="work_quality_rating_Bobby_Paul")
m.addConstr(18.72*x0 + 11.73*x1 + 13.63*x2 >= 61, name="work_quality_rating_all")
m.addConstr(0.15*x1 + 1.88*x2 >= 49, name="likelihood_to_quit_index_Paul_George")
m.addConstr(21.45*x0 + 0.15*x1 >= 25, name="likelihood_to_quit_index_Bobby_Paul")
m.addConstr(21.45*x0 + 0.15*x1 + 1.88*x2 >= 25, name="likelihood_to_quit_index_all")
m.addConstr(5.23*x0 + 17.87*x1 >= 39, name="paperwork_competence_rating_Bobby_Paul")
m.addConstr(17.87*x1 + 20.72*x2 >= 64, name="paperwork_competence_rating_Paul_George")
m.addConstr(5.23*x0 + 20.72*x2 >= 56, name="paperwork_competence_rating_Bobby_George")
m.addConstr(5.23*x0 + 17.87*x1 + 20.72*x2 >= 56, name="paperwork_competence_rating_all")
m.addConstr(21.45*x0 + 0.15*x1 <= 87, name="likelihood_to_quit_index_Bobby_Paul_max")
m.addConstr(0.15*x1 + 1.88*x2 <= 97, name="likelihood_to_quit_index_Paul_George_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print("Hours worked by Bobby:", x0.x)
    print("Hours worked by Paul:", x1.x)
    print("Hours worked by George:", x2.x)
else:
    print("No optimal solution found")
```