## Step 1: Define the symbolic representation of the variables
The variables are ['hours worked by Ringo', 'hours worked by Peggy', 'hours worked by George', 'hours worked by Bobby']. Let's denote them as $x_1, x_2, x_3, x_4$ respectively.

## Step 2: Convert the natural language objects into symbolic variables
The symbolic representation of the variables is:
- $x_1$ : hours worked by Ringo
- $x_2$ : hours worked by Peggy
- $x_3$ : hours worked by George
- $x_4$ : hours worked by Bobby

## 3: Define the objective function in symbolic notation
The objective function to maximize is $4x_1 + 1x_2 + 1x_3 + 6x_4$.

## 4: Define the constraints in symbolic notation
The constraints are:
- $13x_1 \geq 13$ is not correct, it should be $13 = 13$ which is not a constraint but a given condition.
- $2x_2 = 2$ is not correct, it should be $2 = 2$ which is not a constraint but a given condition.
- $12x_3 = 12$ is not correct, it should be $12 = 12$ which is not a constraint but a given condition.
- $19x_4$ has no direct constraint but $19 = 19$.
- $13x_1 + 19x_4 \geq 28$
- $2x_2 + 19x_4 \geq 48$
- $12x_3 + 19x_4 \leq 93$
- $2x_2 + 19x_4 \leq 214$
- $13x_1 + 2x_2 + 12x_3 + 19x_4 \leq 214$
- $x_1$ is continuous
- $x_2$ is integer
- $x_3$ is integer
- $x_4$ is continuous

## 5: Correct and simplify constraints based on given conditions
Given conditions:
- Ringo's organization score is 13, so $13x_1 = 13$ or $x_1 = 1$.
- Peggy has an organization score of 2, so $2x_2 = 2$ or $x_2 = 1$.
- George's organization score is 12, so $12x_3 = 12$ or $x_3 = 1$.
- Bobby's organization score is 19, so $19x_4$ is just $x_4$ as is.

## 6: Apply given conditions to constraints
After applying given conditions:
- The constraints simplify to:
  - $13(1) + 19x_4 \geq 28$ or $13 + 19x_4 \geq 28$
  - $2(1) + 19x_4 \geq 48$ or $2 + 19x_4 \geq 48$
  - $12(1) + 19x_4 \leq 93$ or $12 + 19x_4 \leq 93$
  - $2(1) + 19x_4 \leq 214$ or $2 + 19x_4 \leq 214$
  - $13(1) + 2(1) + 12(1) + 19x_4 \leq 214$ or $27 + 19x_4 \leq 214$

## 7: Further simplify constraints
- $13 + 19x_4 \geq 28$ simplifies to $19x_4 \geq 15$ or $x_4 \geq 15/19$
- $2 + 19x_4 \geq 48$ simplifies to $19x_4 \geq 46$ or $x_4 \geq 46/19$
- $12 + 19x_4 \leq 93$ simplifies to $19x_4 \leq 81$ or $x_4 \leq 81/19$
- $2 + 19x_4 \leq 214$ simplifies to $19x_4 \leq 212$ or $x_4 \leq 212/19$
- $27 + 19x_4 \leq 214$ simplifies to $19x_4 \leq 187$ or $x_4 \leq 187/19$

## 8: Determine the most limiting constraints for $x_4$
- The lower bound for $x_4$ is $max(15/19, 46/19) = 46/19$
- The upper bound for $x_4$ is $min(81/19, 212/19, 187/19) = 81/19$

## 9: Formulate the problem in Gurobi code
```python
import gurobi

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

# Define variables
x1 = m.addVar(lb=1, ub=1, name="Ringo")  # fixed at 1
x2 = m.addVar(lb=1, ub=1, vtype=gurobi.GRB.INTEGER, name="Peggy")  # fixed at 1
x3 = m.addVar(lb=1, ub=1, vtype=gurobi.GRB.INTEGER, name="George")  # fixed at 1
x4 = m.addVar(lb=46/19, ub=81/19, name="Bobby")

# Objective function
m.setObjective(4*x1 + x2 + x3 + 6*x4, gurobi.GRB.MAXIMIZE)

# Solve the problem
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Ringo: ", x1.varValue)
    print("Peggy: ", x2.varValue)
    print("George: ", x3.varValue)
    print("Bobby: ", x4.varValue)
else:
    print("The problem is infeasible")
```

## 10: Symbolic representation
```json
{
    'sym_variables': [('x1', 'hours worked by Ringo'), ('x2', 'hours worked by Peggy'), ('x3', 'hours worked by George'), ('x4', 'hours worked by Bobby')],
    'objective_function': '4*x1 + 1*x2 + 1*x3 + 6*x4',
    'constraints': [
        '13*x1 >= 13',
        '2*x2 >= 2',
        '12*x3 >= 12',
        '19*x4 >= 0',
        '13*x1 + 19*x4 >= 28',
        '2*x2 + 19*x4 >= 48',
        '12*x3 + 19*x4 <= 93',
        '2*x2 + 19*x4 <= 214',
        '13*x1 + 2*x2 + 12*x3 + 19*x4 <= 214'
    ]
}
```