## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Peggy' and 'hours worked by Bobby', which we can denote as $x_0$ and $x_1$ respectively.

## Step 2: Define the symbolic representation of the problem
The objective function to maximize is $2x_0 + 7x_1$.

## Step 3: List all the constraints
The constraints given are:
- $4x_0 + 14x_1 \geq 65$ (total combined organization score minimum)
- $15x_0 + 24x_1 \geq 22$ (total combined work quality rating minimum)
- $19x_0 + 2x_1 \geq 72$ (total combined paperwork competence rating minimum)
- $-4x_0 + 6x_1 \geq 0$ (linear constraint)
- $4x_0 + 14x_1 \leq 119$ (total combined organization score maximum)
- $15x_0 + 24x_1 \leq 59$ (total combined work quality rating maximum)
- $19x_0 + 2x_1 \leq 199$ (total combined paperwork competence rating maximum)

## 4: Consider the variable bounds
- $x_0$ can be a non-integer (continuous variable)
- $x_1$ must be an integer (integer variable)

## 5: Convert the problem into 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
x0 = m.addVar(name="hours_worked_by_Peggy", lb=0)  # Continuous variable
x1 = m.addVar(name="hours_worked_by_Bobby", lb=0, type=gp.GRB.INTEGER)  # Integer variable

# Define the objective function
m.setObjective(2 * x0 + 7 * x1, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(4 * x0 + 14 * x1 >= 65, name="organization_score_min")
m.addConstr(15 * x0 + 24 * x1 >= 22, name="work_quality_rating_min")
m.addConstr(19 * x0 + 2 * x1 >= 72, name="paperwork_competence_rating_min")
m.addConstr(-4 * x0 + 6 * x1 >= 0, name="linear_constraint")
m.addConstr(4 * x0 + 14 * x1 <= 119, name="organization_score_max")
m.addConstr(15 * x0 + 24 * x1 <= 59, name="work_quality_rating_max")
m.addConstr(19 * x0 + 2 * x1 <= 199, name="paperwork_competence_rating_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Peggy: {x0.varValue}")
    print(f"Hours worked by Bobby: {x1.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```

## 6: Symbolic representation of the problem
The symbolic representation is as follows:
```json
{
    'sym_variables': [('x0', 'hours worked by Peggy'), ('x1', 'hours worked by Bobby')],
    'objective_function': '2*x0 + 7*x1',
    'constraints': [
        '4*x0 + 14*x1 >= 65',
        '15*x0 + 24*x1 >= 22',
        '19*x0 + 2*x1 >= 72',
        '-4*x0 + 6*x1 >= 0',
        '4*x0 + 14*x1 <= 119',
        '15*x0 + 24*x1 <= 59',
        '19*x0 + 2*x1 <= 199'
    ]
}
```

```python
import gurobi as gp

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

# Define the variables
x0 = m.addVar(name="hours_worked_by_Peggy", lb=0)  
x1 = m.addVar(name="hours_worked_by_Bobby", lb=0, type=gp.GRB.INTEGER)  

# Define the objective function
m.setObjective(2 * x0 + 7 * x1, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(4 * x0 + 14 * x1 >= 65, name="organization_score_min")
m.addConstr(15 * x0 + 24 * x1 >= 22, name="work_quality_rating_min")
m.addConstr(19 * x0 + 2 * x1 >= 72, name="paperwork_competence_rating_min")
m.addConstr(-4 * x0 + 6 * x1 >= 0, name="linear_constraint")
m.addConstr(4 * x0 + 14 * x1 <= 119, name="organization_score_max")
m.addConstr(15 * x0 + 24 * x1 <= 59, name="work_quality_rating_max")
m.addConstr(19 * x0 + 2 * x1 <= 199, name="paperwork_competence_rating_max")

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Peggy: {x0.varValue}")
    print(f"Hours worked by Bobby: {x1.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```