## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by John', 'hours worked by Hank', 'hours worked by Bobby', and 'hours worked by Dale', which can be represented symbolically as $x_1$, $x_2$, $x_3$, and $x_4$ respectively.

## Step 2: Convert the problem description into a symbolic representation
The objective function to maximize is $1x_1 + 7x_2 + 1x_3 + 1x_4$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $8x_1 \geq 0$ (implicit, as $x_1$ can be fractional and has no direct lower bound given)
- $6x_2 \geq 0$ (implicit, as $x_2$ is a whole number and has no direct lower bound given)
- $11x_3 \geq 0$ (implicit, as $x_3$ can be fractional and has no direct lower bound given)
- $10x_4 \geq 0$ (implicit, as $x_4$ can be fractional and has no direct lower bound given)
- $8x_1 + 10x_4 \geq 37$
- $6x_2 + 11x_3 \geq 35$
- $8x_1 + 10x_4 \leq 158$
- $8x_1 + 6x_2 \leq 109$
- $6x_2 + 11x_3 \leq 193$
- $6x_2 + 10x_4 \leq 103$
- $8x_1 + 6x_2 + 11x_3 \leq 124$
- $8x_1 + 6x_2 + 11x_3 + 10x_4 \leq 124$

## 4: Consider variable bounds and types
- $x_1$ can be fractional
- $x_2$ must be a whole number (integer)
- $x_3$ can be fractional
- $x_4$ can be fractional

## 5: Formulate the problem in Gurobi
To solve this problem using Gurobi, we need to define the model, add variables with their respective types, set the objective function, and add constraints.

## 6: Write the Gurobi code
```python
import gurobi

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

# Define variables
x1 = model.addVar(name='hours_worked_by_John', lb=0, ub=None)  # fractional
x2 = model.addVar(name='hours_worked_by_Hank', lb=0, ub=None, vtype=gurobi.GRB.INTEGER)  # integer
x3 = model.addVar(name='hours_worked_by_Bobby', lb=0, ub=None)  # fractional
x4 = model.addVar(name='hours_worked_by_Dale', lb=0, ub=None)  # fractional

# Set objective function
model.setObjective(1*x1 + 7*x2 + 1*x3 + 1*x4, gurobi.GRB.MAXIMIZE)

# Add constraints
model.addConstr(8*x1 + 10*x4 >= 37)
model.addConstr(6*x2 + 11*x3 >= 35)
model.addConstr(8*x1 + 10*x4 <= 158)
model.addConstr(8*x1 + 6*x2 <= 109)
model.addConstr(6*x2 + 11*x3 <= 193)
model.addConstr(6*x2 + 10*x4 <= 103)
model.addConstr(8*x1 + 6*x2 + 11*x3 <= 124)
model.addConstr(8*x1 + 6*x2 + 11*x3 + 10*x4 <= 124)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print('Objective: ', model.objval)
    print('Hours worked by John: ', x1.varValue)
    print('Hours worked by Hank: ', x2.varValue)
    print('Hours worked by Bobby: ', x3.varValue)
    print('Hours worked by Dale: ', x4.varValue)
else:
    print('The model is infeasible')
```

## 7: Symbolic Representation
```json
{
    'sym_variables': [
        ('x1', 'hours worked by John'),
        ('x2', 'hours worked by Hank'),
        ('x3', 'hours worked by Bobby'),
        ('x4', 'hours worked by Dale')
    ],
    'objective_function': '1*x1 + 7*x2 + 1*x3 + 1*x4',
    'constraints': [
        '8*x1 + 10*x4 >= 37',
        '6*x2 + 11*x3 >= 35',
        '8*x1 + 10*x4 <= 158',
        '8*x1 + 6*x2 <= 109',
        '6*x2 + 11*x3 <= 193',
        '6*x2 + 10*x4 <= 103',
        '8*x1 + 6*x2 + 11*x3 <= 124',
        '8*x1 + 6*x2 + 11*x3 + 10*x4 <= 124'
    ]
}
```