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

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $9.37x_0 + 3.17x_1 + 6.93x_2 + 5.9x_3$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $11x_0 \leq 136$ (work quality rating for Hank)
- $8x_0 \leq 84$ (likelihood to quit index for Hank)
- $6x_1 \leq 136$ (work quality rating for Mary)
- $8x_1 \leq 84$ (likelihood to quit index for Mary)
- $4x_2 \leq 136$ (work quality rating for Dale)
- $6x_2 \leq 84$ (likelihood to quit index for Dale)
- $4x_3 \leq 136$ (work quality rating for Ringo)
- $9x_3 \leq 84$ (likelihood to quit index for Ringo)
- $6x_1 + 4x_3 \geq 26$ (combined work quality rating for Mary and Ringo)
- $11x_0 + 4x_3 \geq 11$ (combined work quality rating for Hank and Ringo)
- $11x_0 + 6x_1 \geq 30$ (combined work quality rating for Hank and Mary)
- $6x_1 + 4x_2 \geq 28$ (combined work quality rating for Mary and Dale)
- $11x_0 + 4x_2 \geq 23$ (combined work quality rating for Hank and Dale)
- $4x_2 + 4x_3 \geq 17$ (combined work quality rating for Dale and Ringo)
- $11x_0 + 6x_1 + 4x_2 + 4x_3 \geq 17$ (combined work quality rating for all)
- $8x_0 + 9x_3 \geq 20$ (combined likelihood to quit index for Hank and Ringo)
- $8x_0 + 8x_1 \geq 13$ (combined likelihood to quit index for Hank and Mary)
- $8x_1 + 6x_2 + 9x_3 \geq 17$ (combined likelihood to quit index for Mary, Dale, and Ringo)
- $8x_0 + 8x_1 + 9x_3 \geq 17$ (combined likelihood to quit index for Hank, Mary, and Ringo)
- $8x_1 + 6x_2 + 9x_3 \geq 11$ (combined likelihood to quit index for Mary, Dale, and Ringo)
- $8x_0 + 8x_1 + 6x_2 + 9x_3 \geq 11$ (combined likelihood to quit index for all)
- $6x_2 - 7x_3 \geq 0$ ( constraint for Dale and Ringo)
- $11x_0 + 6x_1 \leq 77$ (upper bound for combined work quality rating for Hank and Mary)
- $4x_2 + 4x_3 \leq 90$ (upper bound for combined work quality rating for Dale and Ringo)
- $6x_1 + 4x_3 \leq 82$ (upper bound for combined work quality rating for Mary and Ringo)
- $11x_0 + 6x_1 + 4x_2 \leq 48$ (upper bound for combined work quality rating for Hank, Mary, and Dale)
- $11x_0 + 6x_1 + 4x_3 \leq 88$ (upper bound for combined work quality rating for Hank, Mary, and Ringo)
- $8x_0 + 9x_3 \leq 28$ (upper bound for combined likelihood to quit index for Hank and Ringo)
- $8x_1 + 9x_3 \leq 40$ (upper bound for combined likelihood to quit index for Mary and Ringo)
- $8x_0 + 8x_1 + 6x_2 \leq 63$ (upper bound for combined likelihood to quit index for Hank, Mary, and Dale)
- $8x_0 + 8x_1 + 9x_3 \leq 21$ (upper bound for combined likelihood to quit index for Hank, Mary, and Ringo)
- $x_0 \in \mathbb{Z}$ (Hank works whole hours)
- $x_1 \in \mathbb{Z}$ (Mary works whole hours)
- $x_2 \in \mathbb{Z}$ (Dale works whole hours)
- $x_3 \in \mathbb{Z}$ (Ringo works whole hours)

## 4: Convert the problem into Gurobi code
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name='x0', vtype=gurobi.GRB.INTEGER)  # hours worked by Hank
x1 = m.addVar(name='x1', vtype=gurobi.GRB.INTEGER)  # hours worked by Mary
x2 = m.addVar(name='x2', vtype=gurobi.GRB.INTEGER)  # hours worked by Dale
x3 = m.addVar(name='x3', vtype=gurobi.GRB.INTEGER)  # hours worked by Ringo

# Define the objective function
m.setObjective(9.37 * x0 + 3.17 * x1 + 6.93 * x2 + 5.9 * x3, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(11 * x0 <= 136)
m.addConstr(8 * x0 <= 84)
m.addConstr(6 * x1 <= 136)
m.addConstr(8 * x1 <= 84)
m.addConstr(4 * x2 <= 136)
m.addConstr(6 * x2 <= 84)
m.addConstr(4 * x3 <= 136)
m.addConstr(9 * x3 <= 84)

m.addConstr(6 * x1 + 4 * x3 >= 26)
m.addConstr(11 * x0 + 4 * x3 >= 11)
m.addConstr(11 * x0 + 6 * x1 >= 30)
m.addConstr(6 * x1 + 4 * x2 >= 28)
m.addConstr(11 * x0 + 4 * x2 >= 23)
m.addConstr(4 * x2 + 4 * x3 >= 17)
m.addConstr(11 * x0 + 6 * x1 + 4 * x2 + 4 * x3 >= 17)

m.addConstr(8 * x0 + 9 * x3 >= 20)
m.addConstr(8 * x0 + 8 * x1 >= 13)
m.addConstr(8 * x1 + 6 * x2 + 9 * x3 >= 17)
m.addConstr(8 * x0 + 8 * x1 + 9 * x3 >= 17)
m.addConstr(8 * x1 + 6 * x2 + 9 * x3 >= 11)
m.addConstr(8 * x0 + 8 * x1 + 6 * x2 + 9 * x3 >= 11)

m.addConstr(6 * x2 - 7 * x3 >= 0)

m.addConstr(11 * x0 + 6 * x1 <= 77)
m.addConstr(4 * x2 + 4 * x3 <= 90)
m.addConstr(6 * x1 + 4 * x3 <= 82)
m.addConstr(11 * x0 + 6 * x1 + 4 * x2 <= 48)
m.addConstr(11 * x0 + 6 * x1 + 4 * x3 <= 88)

m.addConstr(8 * x0 + 9 * x3 <= 28)
m.addConstr(8 * x1 + 9 * x3 <= 40)
m.addConstr(8 * x0 + 8 * x1 + 6 * x2 <= 63)
m.addConstr(8 * x0 + 8 * x1 + 9 * x3 <= 21)

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', m.objVal)
    print('x0: ', x0.varValue)
    print('x1: ', x1.varValue)
    print('x2: ', x2.varValue)
    print('x3: ', x3.varValue)
else:
    print('No solution found')
```

## 5: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Hank'),
        ('x1', 'hours worked by Mary'),
        ('x2', 'hours worked by Dale'),
        ('x3', 'hours worked by Ringo')
    ],
    'objective_function': '9.37*x0 + 3.17*x1 + 6.93*x2 + 5.9*x3',
    'constraints': [
        '11*x0 <= 136',
        '8*x0 <= 84',
        '6*x1 <= 136',
        '8*x1 <= 84',
        '4*x2 <= 136',
        '6*x2 <= 84',
        '4*x3 <= 136',
        '9*x3 <= 84',
        '6*x1 + 4*x3 >= 26',
        '11*x0 + 4*x3 >= 11',
        '11*x0 + 6*x1 >= 30',
        '6*x1 + 4*x2 >= 28',
        '11*x0 + 4*x2 >= 23',
        '4*x2 + 4*x3 >= 17',
        '11*x0 + 6*x1 + 4*x2 + 4*x3 >= 17',
        '8*x0 + 9*x3 >= 20',
        '8*x0 + 8*x1 >= 13',
        '8*x1 + 6*x2 + 9*x3 >= 17',
        '8*x0 + 8*x1 + 9*x3 >= 17',
        '8*x1 + 6*x2 + 9*x3 >= 11',
        '8*x0 + 8*x1 + 6*x2 + 9*x3 >= 11',
        '6*x2 - 7*x3 >= 0',
        '11*x0 + 6*x1 <= 77',
        '4*x2 + 4*x3 <= 90',
        '6*x1 + 4*x3 <= 82',
        '11*x0 + 6*x1 + 4*x2 <= 48',
        '11*x0 + 6*x1 + 4*x3 <= 88',
        '8*x0 + 9*x3 <= 28',
        '8*x1 + 9*x3 <= 40',
        '8*x0 + 8*x1 + 6*x2 <= 63',
        '8*x0 + 8*x1 + 9*x3 <= 21',
        'x0 ∈ ℤ',
        'x1 ∈ ℤ',
        'x2 ∈ ℤ',
        'x3 ∈ ℤ'
    ]
}
```