## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Laura', 'hours worked by Dale', 'hours worked by Bill', 'hours worked by Jean'].
Let's denote them as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $8.25x_1 + 4.08x_2 + 6.03x_3 + 4.11x_4$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
1. $4x_1 + 10x_3 \geq 14$
2. $10x_3 + 8x_4 \geq 14$
3. $4x_1 + 5x_2 + 10x_3 \geq 12$
4. $4x_1 + 5x_2 + 8x_4 \geq 12$
5. $4x_1 + 5x_2 + 10x_3 \geq 10$
6. $4x_1 + 5x_2 + 8x_4 \geq 10$
7. $4x_1 + 5x_2 + 10x_3 + 8x_4 \geq 10$
8. $x_1 - 9x_4 \geq 0$
9. $4x_1 + 10x_3 \leq 18$
10. $5x_2 + 10x_3 \leq 72$
11. $4x_1 + 5x_2 \leq 28$
12. $x_1$ is an integer
13. $x_3$ is an integer
14. $x_4$ is an integer

## 4: Consider the variable types
- $x_1$ (hours worked by Laura) must be an integer.
- $x_2$ (hours worked by Dale) can be any real number.
- $x_3$ (hours worked by Bill) must be an integer.
- $x_4$ (hours worked by Jean) must be an integer.

## 5: Formulate the problem in Gurobi
We will use Gurobi to solve this optimization problem.

```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x1 = m.addVar(name="hours_worked_by_Laura", vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="hours_worked_by_Dale")
x3 = m.addVar(name="hours_worked_by_Bill", vtype=gp.GRB.INTEGER)
x4 = m.addVar(name="hours_worked_by_Jean", vtype=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(8.25*x1 + 4.08*x2 + 6.03*x3 + 4.11*x4, gp.GRB.MINIMIZE)

# Define the constraints
m.addConstr(4*x1 + 10*x3 >= 14)
m.addConstr(10*x3 + 8*x4 >= 14)
m.addConstr(4*x1 + 5*x2 + 10*x3 >= 12)
m.addConstr(4*x1 + 5*x2 + 8*x4 >= 12)
m.addConstr(4*x1 + 5*x2 + 10*x3 >= 10)
m.addConstr(4*x1 + 5*x2 + 8*x4 >= 10)
m.addConstr(4*x1 + 5*x2 + 10*x3 + 8*x4 >= 10)
m.addConstr(x1 - 9*x4 >= 0)
m.addConstr(4*x1 + 10*x3 <= 18)
m.addConstr(5*x2 + 10*x3 <= 72)
m.addConstr(4*x1 + 5*x2 <= 28)

# Solve the model
m.optimize()

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

## 6: Symbolic Representation
The symbolic representation of the problem is:

```json
{
    'sym_variables': [
        ('x1', 'hours worked by Laura'), 
        ('x2', 'hours worked by Dale'), 
        ('x3', 'hours worked by Bill'), 
        ('x4', 'hours worked by Jean')
    ], 
    'objective_function': '8.25*x1 + 4.08*x2 + 6.03*x3 + 4.11*x4', 
    'constraints': [
        '4*x1 + 10*x3 >= 14', 
        '10*x3 + 8*x4 >= 14', 
        '4*x1 + 5*x2 + 10*x3 >= 12', 
        '4*x1 + 5*x2 + 8*x4 >= 12', 
        '4*x1 + 5*x2 + 10*x3 >= 10', 
        '4*x1 + 5*x2 + 8*x4 >= 10', 
        '4*x1 + 5*x2 + 10*x3 + 8*x4 >= 10', 
        'x1 - 9*x4 >= 0', 
        '4*x1 + 10*x3 <= 18', 
        '5*x2 + 10*x3 <= 72', 
        '4*x1 + 5*x2 <= 28'
    ]
}
```