## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Hank', 'hours worked by Ringo', 'hours worked by Jean', 'hours worked by Mary'] which can be represented symbolically as $x_0, x_1, x_2, x_3$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $9.17x_0 + 1.52x_1 + 4.32x_2 + 7.39x_3$.

## Step 3: List all the constraints in symbolic notation
- $11x_0 \geq 14$ (minimum combined likelihood to quit index from Hank and Jean)
- $7x_1 + 7x_2 \geq 11$ (minimum combined likelihood to quit index from Ringo and Jean)
- $11x_0 + 7x_1 + 3x_3 \geq 15$ (minimum combined likelihood to quit index from Hank, Ringo, and Mary)
- $9x_0 + 3x_1 \geq 26$ (minimum combined work quality rating from Hank and Ringo)
- $9x_0 + 6x_2 \geq 14$ (minimum combined work quality rating from Hank and Jean)
- $2x_2 + 7x_3 \geq 56$ (minimum combined organization score from Jean and Mary)
- $2x_2 + 5x_3 \leq 28$ (maximum combined computer competence rating from Jean and Mary)
- $9x_0 + 2x_2 \leq 63$ (maximum combined computer competence rating from Hank and Jean)
- $4x_1 + 5x_3 \leq 79$ (maximum combined computer competence rating from Ringo and Mary)
- $9x_0 + 4x_1 \leq 63$ (maximum combined computer competence rating from Hank and Ringo)
- $9x_0 + 4x_1 + 2x_2 + 5x_3 \leq 63$ (maximum combined computer competence rating from all)
- $7x_2 + 3x_3 \leq 16$ (maximum combined likelihood to quit index from Jean and Mary)
- $11x_0 + 7x_1 \leq 25$ (maximum combined likelihood to quit index from Hank and Ringo)
- $11x_0 + 7x_1 + 7x_2 + 3x_3 \leq 25$ (maximum combined likelihood to quit index from all)
- $6x_2 + 10x_3 \leq 44$ (maximum combined work quality rating from Jean and Mary)
- $9x_0 + 10x_3 \leq 102$ (maximum combined work quality rating from Hank and Mary)
- $9x_0 + 6x_2 \leq 100$ (maximum combined work quality rating from Hank and Jean)
- $9x_0 + 3x_1 + 6x_2 + 10x_3 \leq 100$ (maximum combined work quality rating from all)
- $2x_0 + 7x_3 \leq 115$ (maximum combined organization score from Hank and Mary)
- $2x_2 + 7x_3 \leq 75$ (maximum combined organization score from Jean and Mary)
- $4x_1 + 2x_2 \leq 84$ (maximum combined organization score from Ringo and Jean)
- $2x_0 + 2x_2 \leq 111$ (maximum combined organization score from Hank and Jean)
- $4x_1 + 7x_3 \leq 105$ (maximum combined organization score from Ringo and Mary)
- $2x_0 + 4x_1 + 2x_2 + 7x_3 \leq 105$ (maximum combined organization score from all)

## 4: Determine the variable types
- $x_0$ (hours worked by Hank) is continuous
- $x_1$ (hours worked by Ringo) is integer
- $x_2$ (hours worked by Jean) is continuous
- $x_3$ (hours worked by Mary) is integer

## 5: Formulate the problem in Gurobi
We will use Gurobi's Python API to formulate and solve this problem.

```python
import gurobi as gp

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

# Define the variables
x0 = m.addVar(lb=0, name="x0")  # hours worked by Hank
x1 = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="x1")  # hours worked by Ringo
x2 = m.addVar(lb=0, name="x2")  # hours worked by Jean
x3 = m.addVar(lb=0, vtype=gp.GRB.INTEGER, name="x3")  # hours worked by Mary

# Define the objective function
m.setObjective(9.17*x0 + 1.52*x1 + 4.32*x2 + 7.39*x3, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(11*x0 + 7*x2 >= 14)  
m.addConstr(7*x1 + 7*x2 >= 11)  
m.addConstr(11*x0 + 7*x1 + 3*x3 >= 15)  
m.addConstr(9*x0 + 3*x1 >= 26)  
m.addConstr(9*x0 + 6*x2 >= 14)  
m.addConstr(2*x2 + 7*x3 >= 56)  
m.addConstr(2*x2 + 5*x3 <= 28)  
m.addConstr(9*x0 + 2*x2 <= 63)  
m.addConstr(4*x1 + 5*x3 <= 79)  
m.addConstr(9*x0 + 4*x1 <= 63)  
m.addConstr(9*x0 + 4*x1 + 2*x2 + 5*x3 <= 63)  
m.addConstr(7*x2 + 3*x3 <= 16)  
m.addConstr(11*x0 + 7*x1 <= 25)  
m.addConstr(11*x0 + 7*x1 + 7*x2 + 3*x3 <= 25)  
m.addConstr(6*x2 + 10*x3 <= 44)  
m.addConstr(9*x0 + 10*x3 <= 102)  
m.addConstr(9*x0 + 6*x2 <= 100)  
m.addConstr(9*x0 + 3*x1 + 6*x2 + 10*x3 <= 100)  
m.addConstr(2*x0 + 7*x3 <= 115)  
m.addConstr(2*x2 + 7*x3 <= 75)  
m.addConstr(4*x1 + 2*x2 <= 84)  
m.addConstr(2*x0 + 2*x2 <= 111)  
m.addConstr(4*x1 + 7*x3 <= 105)  
m.addConstr(2*x0 + 4*x1 + 2*x2 + 7*x3 <= 105)  

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Hank: ", x0.varValue)
    print("Hours worked by Ringo: ", x1.varValue)
    print("Hours worked by Jean: ", x2.varValue)
    print("Hours worked by Mary: ", x3.varValue)
else:
    print("The problem is infeasible")
```

```json
{
    'sym_variables': [
        ['x0', 'hours worked by Hank'], 
        ['x1', 'hours worked by Ringo'], 
        ['x2', 'hours worked by Jean'], 
        ['x3', 'hours worked by Mary']
    ], 
    'objective_function': '9.17*x0 + 1.52*x1 + 4.32*x2 + 7.39*x3', 
    'constraints': [
        '11*x0 + 7*x2 >= 14', 
        '7*x1 + 7*x2 >= 11', 
        '11*x0 + 7*x1 + 3*x3 >= 15', 
        '9*x0 + 3*x1 >= 26', 
        '9*x0 + 6*x2 >= 14', 
        '2*x2 + 7*x3 >= 56', 
        '2*x2 + 5*x3 <= 28', 
        '9*x0 + 2*x2 <= 63', 
        '4*x1 + 5*x3 <= 79', 
        '9*x0 + 4*x1 <= 63', 
        '9*x0 + 4*x1 + 2*x2 + 5*x3 <= 63', 
        '7*x2 + 3*x3 <= 16', 
        '11*x0 + 7*x1 <= 25', 
        '11*x0 + 7*x1 + 7*x2 + 3*x3 <= 25', 
        '6*x2 + 10*x3 <= 44', 
        '9*x0 + 10*x3 <= 102', 
        '9*x0 + 6*x2 <= 100', 
        '9*x0 + 3*x1 + 6*x2 + 10*x3 <= 100', 
        '2*x0 + 7*x3 <= 115', 
        '2*x2 + 7*x3 <= 75', 
        '4*x1 + 2*x2 <= 84', 
        '2*x0 + 2*x2 <= 111', 
        '4*x1 + 7*x3 <= 105', 
        '2*x0 + 4*x1 + 2*x2 + 7*x3 <= 105'
    ]
}
```