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

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $1 \times x_1 + 3 \times x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $0.82x_1 \geq 0.82$ (Laura's organization score constraint, but it seems this is an equality or a given condition rather than an optimization constraint. However, we will consider given conditions and convert optimization constraints properly)
- $1.78x_1 \geq 1.78$ (Laura's productivity rating constraint, similarly, this seems to be a given)
- $0.01x_2 \geq 0.01$ (George's organization score constraint, again, seems like a given)
- $1.34x_2 \geq 1.34$ (George's productivity rating constraint, a given)
- $0.82x_1 + 0.01x_2 \geq 7$ (total combined organization score constraint)
- $1.78x_1 + 1.34x_2 \geq 6$ (total combined productivity rating constraint)
- $7x_1 - 2x_2 \geq 0$ (linear constraint)
- $0.82x_1 + 0.01x_2 \leq 19$ (total combined organization score upper bound)
- $1.78x_1 + 1.34x_2 \leq 22$ (total combined productivity rating upper bound)

## 4: Correct and Clarify Constraints
Given conditions:
- Laura's organization score is 0.82, implying $x_1$ can be any value but her score is fixed.
- Laura's productivity rating is 1.78, similarly, $x_1$ has a fixed productivity rating.
- George's organization score is 0.01.
- George's productivity rating is 1.34.

Optimization constraints:
- $0.82x_1 + 0.01x_2 \geq 7$
- $1.78x_1 + 1.34x_2 \geq 6$
- $7x_1 - 2x_2 \geq 0$
- $0.82x_1 + 0.01x_2 \leq 19$
- $1.78x_1 + 1.34x_2 \leq 22$
- $x_2$ must be an integer.

## 5: Symbolic Representation
```json
{
'sym_variables': [('x1', 'hours worked by Laura'), ('x2', 'hours worked by George')],
'objective_function': '1*x1 + 3*x2',
'constraints': [
    '0.82*x1 + 0.01*x2 >= 7',
    '1.78*x1 + 1.34*x2 >= 6',
    '7*x1 - 2*x2 >= 0',
    '0.82*x1 + 0.01*x2 <= 19',
    '1.78*x1 + 1.34*x2 <= 22'
]
}
```

## 6: Gurobi Code
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define variables
    x1 = model.addVar(name="hours_worked_by_Laura", lb=0)  # Assuming hours cannot be negative
    x2 = model.addVar(name="hours_worked_by_George", lb=0, vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(1 * x1 + 3 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(0.82 * x1 + 0.01 * x2 >= 7)
    model.addConstr(1.78 * x1 + 1.34 * x2 >= 6)
    model.addConstr(7 * x1 - 2 * x2 >= 0)
    model.addConstr(0.82 * x1 + 0.01 * x2 <= 19)
    model.addConstr(1.78 * x1 + 1.34 * x2 <= 22)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Laura: {x1.varValue}")
        print(f"Hours worked by George: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("The model is infeasible.")
    else:
        print("The model has a non-optimal status.")

solve_optimization_problem()
```