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

## Step 2: Convert the natural language description into a symbolic representation
The symbolic representation of the variables is:
- $x_1$ : hours worked by Mary
- $x_2$ : hours worked by Paul
- $x_3$ : hours worked by Bobby

## 3: Define the objective function in symbolic notation
The objective function to minimize is $1.38x_1 + 7.91x_2 + 2.21x_3$.

## 4: Define the constraints in symbolic notation
The constraints are:
- $1x_1 \leq 130$ (organization score constraint for Mary, but it's an attribute, not a direct constraint)
- $8x_2 \leq 130$ (organization score constraint for Paul, but it's an attribute, not a direct constraint)
- $11x_3 \leq 130$ (organization score constraint for Bobby, but it's an attribute, not a direct constraint)
- $1x_1 + 11x_3 \geq 42$
- $1x_1 + 8x_2 \geq 14$
- $1x_1 + 8x_2 + 11x_3 \geq 25$
- $-5x_1 + 5x_3 \geq 0$
- $8x_2 + 11x_3 \leq 80$
- $x_1$ can be fractional
- $x_2$ must be an integer
- $x_3$ can be fractional

## 5: Correctly interpret the organization score constraints
The organization scores are attributes: 
- Mary's organization score is 1.
- Paul's organization score is 8.
- Bobby's organization score is 11.

These are not constraints but rather attributes of $x_1$, $x_2$, and $x_3$. The actual constraints from the problem statement regarding organization scores are:
- $1x_1 + 11x_3 \geq 42$
- $1x_1 + 8x_2 \geq 14$
- $1x_1 + 8x_2 + 11x_3 \geq 25$

And the upper bounds for organization scores are implicitly given but not directly used as constraints in the traditional sense.

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

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

# Define the variables
x1 = m.addVar(name="hours_worked_by_Mary", lb=0)  # Mary can work fractional hours
x2 = m.addVar(name="hours_worked_by_Paul", lb=0, vtype=gurobi.GRB.INTEGER)  # Paul must work integer hours
x3 = m.addVar(name="hours_worked_by_Bobby", lb=0)  # Bobby can work fractional hours

# Objective function
m.setObjective(1.38*x1 + 7.91*x2 + 2.21*x3, gurobi.GRB.MINIMIZE)

# Constraints
m.addConstr(x1 + 11*x3 >= 42, name="combined_Mary_Bobby_score")
m.addConstr(x1 + 8*x2 >= 14, name="combined_Mary_Paul_score")
m.addConstr(x1 + 8*x2 + 11*x3 >= 25, name="combined_score")
m.addConstr(-5*x1 + 5*x3 >= 0, name="Mary_Bobby_hours")
m.addConstr(8*x2 + 11*x3 <= 80, name="Paul_Bobby_score")

# Solve the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Mary: {x1.varValue}")
    print(f"Hours worked by Paul: {x2.varValue}")
    print(f"Hours worked by Bobby: {x3.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```

## 7: Symbolic representation in JSON format
```json
{
    "sym_variables": [
        ["x1", "hours worked by Mary"],
        ["x2", "hours worked by Paul"],
        ["x3", "hours worked by Bobby"]
    ],
    "objective_function": "1.38x1 + 7.91x2 + 2.21x3",
    "constraints": [
        "x1 + 11x3 >= 42",
        "x1 + 8x2 >= 14",
        "x1 + 8x2 + 11x3 >= 25",
        "-5x1 + 5x3 >= 0",
        "8x2 + 11x3 <= 80"
    ]
}
```