## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'hours worked by John' and 'hours worked by George'. Let's denote 'hours worked by John' as $x_1$ and 'hours worked by George' as $x_2$. The objective function to minimize is $3x_1 + x_2$.

## Step 2: List the constraints in symbolic notation
The constraints given are:
- John's productivity rating is 14: $14x_1$
- John's computer competence rating is 14: $14x_1$
- John's organization score is 11: $11x_1$
- George's productivity rating is 17: $17x_2$
- George's computer competence rating is 4: $4x_2$
- George's organization score is 20: $20x_2$
- Total combined productivity rating $\geq 39$: $14x_1 + 17x_2 \geq 39$
- Total combined computer competence rating $\geq 21$: $14x_1 + 4x_2 \geq 21$
- Total combined organization score $\geq 66$: $11x_1 + 20x_2 \geq 66$
- $2x_1 - 7x_2 \geq 0$
- Total combined productivity rating $\leq 106$: $14x_1 + 17x_2 \leq 106$
- Total combined computer competence rating $\leq 55$: $14x_1 + 4x_2 \leq 55$
- Total combined organization score $\leq 131$: $11x_1 + 20x_2 \leq 131$

## 3: Define the symbolic representation
The symbolic variables are:
- $x_1$ for 'hours worked by John'
- $x_2$ for 'hours worked by George'

The objective function is: $3x_1 + x_2$

The constraints are:
1. $14x_1 + 17x_2 \geq 39$
2. $14x_1 + 4x_2 \geq 21$
3. $11x_1 + 20x_2 \geq 66$
4. $2x_1 - 7x_2 \geq 0$
5. $14x_1 + 17x_2 \leq 106$
6. $14x_1 + 4x_2 \leq 55$
7. $11x_1 + 20x_2 \leq 131$

## 4: Convert to Gurobi code
```python
import gurobi

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

# Define the variables
x1 = m.addVar(name='hours_worked_by_John', lb=0)  # Assuming hours cannot be negative
x2 = m.addVar(name='hours_worked_by_George', lb=0)  # Assuming hours cannot be negative

# Define the objective function
m.setObjective(3 * x1 + x2, gurobi.GRB.MINIMIZE)

# Add constraints
m.addConstr(14 * x1 + 17 * x2 >= 39)
m.addConstr(14 * x1 + 4 * x2 >= 21)
m.addConstr(11 * x1 + 20 * x2 >= 66)
m.addConstr(2 * x1 - 7 * x2 >= 0)
m.addConstr(14 * x1 + 17 * x2 <= 106)
m.addConstr(14 * x1 + 4 * x2 <= 55)
m.addConstr(11 * x1 + 20 * x2 <= 131)

# Optimize the model
m.optimize()

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

## 5: Symbolic Representation in JSON format
```json
{
    'sym_variables': [('x1', 'hours worked by John'), ('x2', 'hours worked by George')],
    'objective_function': '3*x1 + x2',
    'constraints': [
        '14*x1 + 17*x2 >= 39',
        '14*x1 + 4*x2 >= 21',
        '11*x1 + 20*x2 >= 66',
        '2*x1 - 7*x2 >= 0',
        '14*x1 + 17*x2 <= 106',
        '14*x1 + 4*x2 <= 55',
        '11*x1 + 20*x2 <= 131'
    ]
}
```