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

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $7.06x_0 + 2.87x_1 + 5.24x_2$.

## Step 3: List the constraints in symbolic notation
The constraints given are:
- $18.72x_0 \leq 206$
- $21.45x_0 \leq 194$
- $5.23x_0 \leq 232$
- $11.73x_1 \leq 206$
- $0.15x_1 \leq 194$
- $17.87x_1 \leq 232$
- $13.63x_2 \leq 206$
- $1.88x_2 \leq 194$
- $20.72x_2 \leq 232$
- $18.72x_0 + 11.73x_1 \geq 61$
- $18.72x_0 + 11.73x_1 + 13.63x_2 \geq 61$
- $0.15x_1 + 1.88x_2 \geq 49$
- $21.45x_0 + 0.15x_1 \geq 25$
- $21.45x_0 + 0.15x_1 + 1.88x_2 \geq 25$
- $5.23x_0 + 17.87x_1 \geq 39$
- $17.87x_1 + 20.72x_2 \geq 64$
- $5.23x_0 + 20.72x_2 \geq 56$
- $5.23x_0 + 17.87x_1 + 20.72x_2 \geq 56$
- $21.45x_0 + 0.15x_1 \leq 87$
- $0.15x_1 + 1.88x_2 \leq 97$

## Step 4: Consider the variable restrictions
- $x_0$ is not restricted to integers.
- $x_1$ is not restricted to integers.
- $x_2$ must be a whole number (integer).

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

# Define the model
model = gurobi.Model()

# Define the variables
x0 = model.addVar(name="x0", lb=0)  # hours worked by Bobby
x1 = model.addVar(name="x1", lb=0)  # hours worked by Paul
x2 = model.addVar(name="x2", lb=0, vtype=gurobi.GRB.INTEGER)  # hours worked by George

# Define the objective function
model.setObjective(7.06 * x0 + 2.87 * x1 + 5.24 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(18.72 * x0 <= 206)
model.addConstr(21.45 * x0 <= 194)
model.addConstr(5.23 * x0 <= 232)
model.addConstr(11.73 * x1 <= 206)
model.addConstr(0.15 * x1 <= 194)
model.addConstr(17.87 * x1 <= 232)
model.addConstr(13.63 * x2 <= 206)
model.addConstr(1.88 * x2 <= 194)
model.addConstr(20.72 * x2 <= 232)
model.addConstr(18.72 * x0 + 11.73 * x1 >= 61)
model.addConstr(18.72 * x0 + 11.73 * x1 + 13.63 * x2 >= 61)
model.addConstr(0.15 * x1 + 1.88 * x2 >= 49)
model.addConstr(21.45 * x0 + 0.15 * x1 >= 25)
model.addConstr(21.45 * x0 + 0.15 * x1 + 1.88 * x2 >= 25)
model.addConstr(5.23 * x0 + 17.87 * x1 >= 39)
model.addConstr(17.87 * x1 + 20.72 * x2 >= 64)
model.addConstr(5.23 * x0 + 20.72 * x2 >= 56)
model.addConstr(5.23 * x0 + 17.87 * x1 + 20.72 * x2 >= 56)
model.addConstr(21.45 * x0 + 0.15 * x1 <= 87)
model.addConstr(0.15 * x1 + 1.88 * x2 <= 97)

# Solve the model
model.optimize()

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

## 6: Symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'hours worked by Bobby'), 
        ('x1', 'hours worked by Paul'), 
        ('x2', 'hours worked by George')
    ], 
    'objective_function': '7.06*x0 + 2.87*x1 + 5.24*x2', 
    'constraints': [
        '18.72*x0 <= 206',
        '21.45*x0 <= 194',
        '5.23*x0 <= 232',
        '11.73*x1 <= 206',
        '0.15*x1 <= 194',
        '17.87*x1 <= 232',
        '13.63*x2 <= 206',
        '1.88*x2 <= 194',
        '20.72*x2 <= 232',
        '18.72*x0 + 11.73*x1 >= 61',
        '18.72*x0 + 11.73*x1 + 13.63*x2 >= 61',
        '0.15*x1 + 1.88*x2 >= 49',
        '21.45*x0 + 0.15*x1 >= 25',
        '21.45*x0 + 0.15*x1 + 1.88*x2 >= 25',
        '5.23*x0 + 17.87*x1 >= 39',
        '17.87*x1 + 20.72*x2 >= 64',
        '5.23*x0 + 20.72*x2 >= 56',
        '5.23*x0 + 17.87*x1 + 20.72*x2 >= 56',
        '21.45*x0 + 0.15*x1 <= 87',
        '0.15*x1 + 1.88*x2 <= 97'
    ]
}
```