## Step 1: Define the symbolic representation of the problem
The problem involves maximizing an objective function subject to several constraints. The variables are:
- $x_1$: hours worked by Hank
- $x_2$: hours worked by Ringo
- $x_3$: hours worked by Paul
- $x_4$: hours worked by Laura

The objective function to maximize is: $9.01x_1 + 2.2x_2 + 5.01x_3 + 4.0x_4$

## Step 2: List the constraints in symbolic notation
The constraints given are:
- $2x_1 \leq 130$
- $13x_2 \leq 130$
- $13x_3 \leq 130$
- $8x_4 \leq 130$
- $13x_2 + 8x_4 \geq 23$
- $2x_1 + 13x_3 \geq 22$
- $2x_1 + 8x_4 \geq 10$
- $13x_2 + 13x_3 + 8x_4 \geq 19$
- $2x_1 + 8x_4 \leq 101$
- $13x_3 + 8x_4 \leq 74$
- $2x_1 + 13x_3 \leq 86$
- $2x_1 + 13x_2 \leq 120$
- $13x_2 + 8x_4 \leq 91$
- $13x_2 + 13x_3 \leq 119$
- $2x_1 + 13x_2 + 8x_4 \leq 47$
- $13x_2 + 13x_3 + 8x_4 \leq 90$
- $2x_1 + 13x_2 + 13x_3 + 8x_4 \leq 90$
- $x_1, x_2, x_3, x_4$ are integers

## 3: Convert the problem into a Gurobi model
We will use the Gurobi Python API to model and solve this problem.

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define the variables
x1 = m.addVar(name="x1", vtype=gp.GRB.INTEGER)  # hours worked by Hank
x2 = m.addVar(name="x2", vtype=gp.GRB.INTEGER)  # hours worked by Ringo
x3 = m.addVar(name="x3", vtype=gp.GRB.INTEGER)  # hours worked by Paul
x4 = m.addVar(name="x4", vtype=gp.GRB.INTEGER)  # hours worked by Laura

# Define the objective function
m.setObjective(9.01 * x1 + 2.2 * x2 + 5.01 * x3 + 4.0 * x4, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(2 * x1 <= 130)
m.addConstr(13 * x2 <= 130)
m.addConstr(13 * x3 <= 130)
m.addConstr(8 * x4 <= 130)

m.addConstr(13 * x2 + 8 * x4 >= 23)
m.addConstr(2 * x1 + 13 * x3 >= 22)
m.addConstr(2 * x1 + 8 * x4 >= 10)
m.addConstr(13 * x2 + 13 * x3 + 8 * x4 >= 19)

m.addConstr(2 * x1 + 8 * x4 <= 101)
m.addConstr(13 * x3 + 8 * x4 <= 74)
m.addConstr(2 * x1 + 13 * x3 <= 86)
m.addConstr(2 * x1 + 13 * x2 <= 120)
m.addConstr(13 * x2 + 8 * x4 <= 91)
m.addConstr(13 * x2 + 13 * x3 <= 119)

m.addConstr(2 * x1 + 13 * x2 + 8 * x4 <= 47)
m.addConstr(13 * x2 + 13 * x3 + 8 * x4 <= 90)
m.addConstr(2 * x1 + 13 * x2 + 13 * x3 + 8 * x4 <= 90)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Hank: ", x1.varValue)
    print("Hours worked by Ringo: ", x2.varValue)
    print("Hours worked by Paul: ", x3.varValue)
    print("Hours worked by Laura: ", x4.varValue)
else:
    print("The problem is infeasible")
```

## Step 4: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x1', 'hours worked by Hank'), 
        ('x2', 'hours worked by Ringo'), 
        ('x3', 'hours worked by Paul'), 
        ('x4', 'hours worked by Laura')
    ], 
    'objective_function': '9.01x1 + 2.2x2 + 5.01x3 + 4.0x4', 
    'constraints': [
        '2x1 <= 130', 
        '13x2 <= 130', 
        '13x3 <= 130', 
        '8x4 <= 130', 
        '13x2 + 8x4 >= 23', 
        '2x1 + 13x3 >= 22', 
        '2x1 + 8x4 >= 10', 
        '13x2 + 13x3 + 8x4 >= 19', 
        '2x1 + 8x4 <= 101', 
        '13x3 + 8x4 <= 74', 
        '2x1 + 13x3 <= 86', 
        '2x1 + 13x2 <= 120', 
        '13x2 + 8x4 <= 91', 
        '13x2 + 13x3 <= 119', 
        '2x1 + 13x2 + 8x4 <= 47', 
        '13x2 + 13x3 + 8x4 <= 90', 
        '2x1 + 13x2 + 13x3 + 8x4 <= 90'
    ]
}
```