## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Ringo' and 'hours worked by John', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to minimize is $9x_1 + 2x_2$.

## Step 3: List the constraints
The constraints given are:
- $6x_1 + 12x_2 \geq 52$
- $7x_1 + 11x_2 \geq 52$
- $5x_1 + 11x_2 \geq 21$
- $9x_1 + 14x_2 \geq 21$
- $-8x_1 + 5x_2 \geq 0$
- $6x_1 + 12x_2 \leq 94$
- $7x_1 + 11x_2 \leq 70$
- $5x_1 + 11x_2 \leq 61$
- $9x_1 + 14x_2 \leq 37$
- $x_1$ is an integer
- $x_2$ can be fractional

## 4: Convert the problem into a Gurobi code
We will use Gurobi's Python API to model and solve this problem.

```python
import gurobi as gp

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

# Define the variables
x1 = m.addVar(name="hours_worked_by_Ringo", vtype=gp.GRB.INTEGER)  # integer
x2 = m.addVar(name="hours_worked_by_John")  # continuous

# Define the objective function
m.setObjective(9 * x1 + 2 * x2, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(6 * x1 + 12 * x2 >= 52)
m.addConstr(7 * x1 + 11 * x2 >= 52)
m.addConstr(5 * x1 + 11 * x2 >= 21)
m.addConstr(9 * x1 + 14 * x2 >= 21)
m.addConstr(-8 * x1 + 5 * x2 >= 0)
m.addConstr(6 * x1 + 12 * x2 <= 94)
m.addConstr(7 * x1 + 11 * x2 <= 70)
m.addConstr(5 * x1 + 11 * x2 <= 61)
m.addConstr(9 * x1 + 14 * x2 <= 37)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Ringo: {x1.varValue}")
    print(f"Hours worked by John: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```

## 5: Symbolic Representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'hours worked by Ringo'), ('x2', 'hours worked by John')],
    'objective_function': '9*x1 + 2*x2',
    'constraints': [
        '6*x1 + 12*x2 >= 52',
        '7*x1 + 11*x2 >= 52',
        '5*x1 + 11*x2 >= 21',
        '9*x1 + 14*x2 >= 21',
        '-8*x1 + 5*x2 >= 0',
        '6*x1 + 12*x2 <= 94',
        '7*x1 + 11*x2 <= 70',
        '5*x1 + 11*x2 <= 61',
        '9*x1 + 14*x2 <= 37'
    ]
}
```

```python
import gurobi as gp

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

# Define the variables
x1 = m.addVar(name="hours_worked_by_Ringo", vtype=gp.GRB.INTEGER)  # integer
x2 = m.addVar(name="hours_worked_by_John")  # continuous

# Define the objective function
m.setObjective(9 * x1 + 2 * x2, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(6 * x1 + 12 * x2 >= 52)
m.addConstr(7 * x1 + 11 * x2 >= 52)
m.addConstr(5 * x1 + 11 * x2 >= 21)
m.addConstr(9 * x1 + 14 * x2 >= 21)
m.addConstr(-8 * x1 + 5 * x2 >= 0)
m.addConstr(6 * x1 + 12 * x2 <= 94)
m.addConstr(7 * x1 + 11 * x2 <= 70)
m.addConstr(5 * x1 + 11 * x2 <= 61)
m.addConstr(9 * x1 + 14 * x2 <= 37)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Ringo: {x1.varValue}")
    print(f"Hours worked by John: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```