## Step 1: Define the variables
The variables are defined as follows:
- hours worked by Jean: $x_0$
- hours worked by Peggy: $x_1$
- hours worked by Hank: $x_2$
- hours worked by Paul: $x_3$
- hours worked by John: $x_4$
- hours worked by George: $x_5$

## Step 2: Define the objective function
The objective function to maximize is:
$3.94x_0 + 2.48x_1 + 4.93x_2 + 6.64x_3 + 1.7x_4 + 5.4x_5$

## Step 3: Define the constraints
The constraints are defined based on the given problem description.

### Resource constraints
- $18x_0 + 1x_1 + 26x_2 + 14x_3 + 10x_4 + 18x_5 \leq 267$ (computer competence rating)
- $10x_0 + 17x_1 + 15x_2 + 13x_3 + 17x_4 + 24x_5 \leq 268$ (likelihood to quit index)

### Individual constraints
- $18x_0 = 18$
- $10x_0 = 10$
- $1x_1 = 1$
- $17x_1 = 17$
- $26x_2 = 26$
- $15x_2 = 15$
- $14x_3 = 14$
- $13x_3 = 13$
- $10x_4 = 10$
- $17x_4 = 17$
- $18x_5 = 18$
- $24x_5 = 24$

### Combined computer competence rating constraints
- $14x_3 + 10x_4 \geq 14$
- $26x_2 + 18x_5 \geq 20$
- $1x_1 + 18x_5 \geq 39$
- $18x_0 + 10x_4 \geq 18$
- $18x_0 + 1x_1 + 10x_4 \geq 32$
- $26x_2 + 10x_4 + 18x_5 \geq 32$
- $1x_1 + 10x_4 + 18x_5 \geq 32$
- $26x_2 + 14x_3 + 18x_5 \geq 32$
- $1x_1 + 14x_3 + 10x_4 \geq 32$
- $1x_1 + 26x_2 + 10x_4 \geq 32$
- $18x_0 + 1x_1 + 10x_4 \geq 34$
- $26x_2 + 10x_4 + 18x_5 \geq 34$
- $1x_1 + 10x_4 + 18x_5 \geq 34$
- $26x_2 + 14x_3 + 18x_5 \geq 34$

### Combined likelihood to quit index constraints
- $10x_0 + 13x_3 \geq 29$
- $15x_2 + 17x_4 \geq 38$
- $10x_0 + 17x_4 \geq 17$
- $17x_1 + 15x_2 \geq 16$
- $15x_2 + 13x_3 \geq 22$
- $13x_3 + 24x_5 \geq 44$
- $17x_1 + 13x_3 \geq 20$
- $10x_0 + 24x_5 \geq 35$
- $17x_1 + 15x_2 + 13x_3 \geq 43$
- $17x_1 + 13x_3 + 10x_4 \geq 43$
- $10x_0 + 13x_3 + 10x_4 \geq 43$
- $10x_0 + 17x_1 + 15x_2 \geq 43$
- $15x_2 + 17x_4 + 24x_5 \geq 43$
- $15x_2 + 13x_3 + 24x_5 \geq 43$
- $17x_1 + 15x_2 + 24x_5 \geq 43$
- $17x_1 + 13x_3 + 24x_5 \geq 43$
- $10x_0 + 17x_1 + 15x_2 \geq 42$
- $17x_1 + 13x_3 + 10x_4 \geq 42$
- $10x_0 + 13x_3 + 10x_4 \geq 42$
- $10x_0 + 17x_1 + 15x_2 \geq 42$
- $15x_2 + 17x_4 + 24x_5 \geq 42$
- $15x_2 + 13x_3 + 24x_5 \geq 42$
- $17x_1 + 15x_2 + 24x_5 \geq 42$
- $17x_1 + 13x_3 + 24x_5 \geq 42$

### Upper bound constraints
- $18x_0 \leq 267$
- $1x_1 \leq 267$
- $26x_2 \leq 267$
- $14x_3 \leq 267$
- $10x_4 \leq 267$
- $18x_5 \leq 267$

## Step 4: Implement in Gurobi
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(lb=0, name="hours_worked_by_Jean")
    x1 = model.addVar(lb=0, name="hours_worked_by_Peggy")
    x2 = model.addVar(lb=0, name="hours_worked_by_Hank")
    x3 = model.addVar(lb=0, name="hours_worked_by_Paul")
    x4 = model.addVar(lb=0, name="hours_worked_by_John")
    x5 = model.addVar(lb=0, name="hours_worked_by_George")

    # Objective function
    model.setObjective(3.94*x0 + 2.48*x1 + 4.93*x2 + 6.64*x3 + 1.7*x4 + 5.4*x5, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(18*x0 + x1 + 26*x2 + 14*x3 + 10*x4 + 18*x5 <= 267)
    model.addConstr(10*x0 + 17*x1 + 15*x2 + 13*x3 + 17*x4 + 24*x5 <= 268)

    model.addConstr(x0 == 1)
    model.addConstr(x1 == 1)
    model.addConstr(x2 == 26/26)
    model.addConstr(x3 == 14/14)
    model.addConstr(x4 == 10/17)
    model.addConstr(x5 == 18/24)

    # Add other constraints here...

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Hours worked by Jean: ", x0.varValue)
        print("Hours worked by Peggy: ", x1.varValue)
        print("Hours worked by Hank: ", x2.varValue)
        print("Hours worked by Paul: ", x3.varValue)
        print("Hours worked by John: ", x4.varValue)
        print("Hours worked by George: ", x5.varValue)
    else:
        print("No solution found")

optimization_problem()
```
The final answer is: 
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(lb=0, name="hours_worked_by_Jean")
    x1 = model.addVar(lb=0, name="hours_worked_by_Peggy")
    x2 = model.addVar(lb=0, name="hours_worked_by_Hank")
    x3 = model.addVar(lb=0, name="hours_worked_by_Paul")
    x4 = model.addVar(lb=0, name="hours_worked_by_John")
    x5 = model.addVar(lb=0, name="hours_worked_by_George")

    # Objective function
    model.setObjective(3.94*x0 + 2.48*x1 + 4.93*x2 + 6.64*x3 + 1.7*x4 + 5.4*x5, gurobi.GRB.MAXIMIZE)

    # Individual constraints
    model.addConstr(x0 == 1, name='jean_hours')
    model.addConstr(x1 == 1, name='peggy_hours')
    model.addConstr(x2 == 1, name='hank_hours')
    model.addConstr(x3 == 1, name='paul_hours')
    model.addConstr(x4 == 1, name='john_hours')
    model.addConstr(x5 == 1, name='george_hours')

    model.addConstr(18*x0 + 1*x1 + 26*x2 + 14*x3 + 10*x4 + 18*x5 <= 267)
    model.addConstr(10*x0 + 17*x1 + 15*x2 + 13*x3 + 17*x4 + 24*x5 <= 268)

    # Computer competence rating constraints
    model.addConstr(18*x0 + x1 + 26*x2 + 14*x3 + 10*x4 + 18*x5 <= 267)
    model.addConstr(18*x0 <= 18)
    model.addConstr(x1 <= 1)
    model.addConstr(26*x2 <= 26)
    model.addConstr(14*x3 <= 14)
    model.addConstr(10*x4 <= 10)
    model.addConstr(18*x5 <= 18)

    model.addConstr(14*x3 + 10*x4 >= 14)
    model.addConstr(26*x2 + 18*x5 >= 20)
    model.addConstr(x1 + 18*x5 >= 39)
    model.addConstr(18*x0 + 10*x4 >= 18)
    model.addConstr(18*x0 + x1 + 10*x4 >= 32)

    # Likelihood to quit index constraints
    model.addConstr(10*x0 + 13*x3 >= 29)
    model.addConstr(15*x2 + 17*x4 >= 38)
    model.addConstr(10*x0 + 17*x4 >= 17)
    model.addConstr(17*x1 + 15*x2 >= 16)
    model.addConstr(15*x2 + 13*x3 >= 22)
    model.addConstr(13*x3 + 24*x5 >= 44)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
    else:
        print("No solution found")

optimization_problem()
```