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

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_0$ : hours worked by Hank
- $x_1$ : hours worked by Bill
- $x_2$ : hours worked by Dale

## Step 3: Define the objective function in symbolic notation
The objective function to minimize is $7.28x_0 + 5.42x_1 + 5.65x_2$.

## 4: List the constraints in symbolic notation
The constraints are:
- $1x_0 \leq 104$ (work quality rating for Hank, but it's given as a fixed value, so it's not a constraint in the traditional sense)
- $1x_1 \leq 104$ (work quality rating for Bill, but it's given as a fixed value, so it's not a constraint in the traditional sense)
- $9x_2 \leq 104$ (work quality rating for Dale, but it's given as a fixed value, so it's not a constraint in the traditional sense)
- $1x_0 \leq 83$ (paperwork competence rating for Hank, but it's given as a fixed value, so it's not a constraint in the traditional sense)
- $9x_1 \leq 83$ (paperwork competence rating for Bill, but it's given as a fixed value, so it's not a constraint in the traditional sense)
- $5x_2 \leq 83$ (paperwork competence rating for Dale, but it's given as a fixed value, so it's not a constraint in the traditional sense)
- $1x_0 + 9x_2 \geq 24$ (combined work quality rating from Hank and Dale)
- $1x_0 + 11x_1 + 9x_2 \geq 24$ (combined work quality rating from Hank, Bill, and Dale)
- $1x_0 + 9x_1 \geq 22$ (combined paperwork competence rating from Hank and Bill)
- $9x_1 + 5x_2 \geq 25$ (combined paperwork competence rating from Bill and Dale)
- $1x_0 + 5x_2 \geq 19$ (combined paperwork competence rating from Hank and Dale)
- $1x_0 + 9x_1 + 5x_2 \geq 18$ (combined paperwork competence rating from Hank, Bill, and Dale, but this is less than the previous, so it's redundant)
- $-9x_0 + 4x_1 \geq 0$ (relationship between Hank and Bill's hours)
- $-8x_1 + 3x_2 \geq 0$ (relationship between Bill and Dale's hours)
- $1x_0 + 11x_1 \leq 77$ (combined work quality rating from Hank and Bill)
- $1x_0 + 9x_2 \leq 55$ (combined work quality rating from Hank and Dale)
- $9x_1 + 5x_2 \leq 38$ (combined paperwork competence rating from Bill and Dale)
- $1x_0 + 9x_1 \leq 33$ (combined paperwork competence rating from Hank and Bill)

## 5: Create the Gurobi model and variables
We will now create a Gurobi model and define the variables.

## 6: Implement the objective function and constraints in Gurobi
```python
import gurobi

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

# Define the variables
x0 = m.addVar(name="x0", lb=0)  # hours worked by Hank
x1 = m.addVar(name="x1", lb=0)  # hours worked by Bill
x2 = m.addVar(name="x2", lb=0)  # hours worked by Dale

# Define the objective function
m.setObjective(7.28 * x0 + 5.42 * x1 + 5.65 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(x0 + 9 * x2 >= 24)  
m.addConstr(x0 + 11 * x1 + 9 * x2 >= 24)  
m.addConstr(x0 + 9 * x1 >= 22)  
m.addConstr(9 * x1 + 5 * x2 >= 25)  
m.addConstr(x0 + 5 * x2 >= 19)  
m.addConstr(x0 + 9 * x1 + 5 * x2 >= 18)  
m.addConstr(-9 * x0 + 4 * x1 >= 0)  
m.addConstr(-8 * x1 + 3 * x2 >= 0)  
m.addConstr(x0 + 11 * x1 <= 77)  
m.addConstr(x0 + 9 * x2 <= 55)  
m.addConstr(9 * x1 + 5 * x2 <= 38)  
m.addConstr(x0 + 9 * x1 <= 33)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objval)
    print("Hours worked by Hank: ", x0.varValue)
    print("Hours worked by Bill: ", x1.varValue)
    print("Hours worked by Dale: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 7: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x0', 'hours worked by Hank'), ('x1', 'hours worked by Bill'), ('x2', 'hours worked by Dale')],
    'objective_function': '7.28*x0 + 5.42*x1 + 5.65*x2',
    'constraints': [
        'x0 + 9*x2 >= 24',
        'x0 + 11*x1 + 9*x2 >= 24',
        'x0 + 9*x1 >= 22',
        '9*x1 + 5*x2 >= 25',
        'x0 + 5*x2 >= 19',
        'x0 + 9*x1 + 5*x2 >= 18',
        '-9*x0 + 4*x1 >= 0',
        '-8*x1 + 3*x2 >= 0',
        'x0 + 11*x1 <= 77',
        'x0 + 9*x2 <= 55',
        '9*x1 + 5*x2 <= 38',
        'x0 + 9*x1 <= 33'
    ]
}
```