## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by George' and 'hours worked by Dale', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $7x_1 + 7x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $5x_1 + 3x_2 \geq 14$ (combined paperwork competence rating)
- $15x_1 + 9x_2 \geq 14$ (combined computer competence rating)
- $x_1 - 7x_2 \geq 0$ (given constraint)
- $5x_1 + 3x_2 \leq 45$ (paperwork upper bound)
- $15x_1 + 9x_2 \leq 50$ (computer upper bound)
- $x_1, x_2 \geq 0$ (non-negativity, implicitly assumed as hours cannot be negative)

## 4: Correct and Simplify Constraints
Upon review, notice that the lower bounds for paperwork and computer competence ratings are repeated with the same value (14), and there are upper bounds given for the resources:
- Paperwork: $5x_1 + 3x_2 \leq 60$
- Computer: $15x_1 + 9x_2 \leq 64$

These should replace the previously listed constraints of the same nature.

## 5: Symbolic Representation
The symbolic representation of the problem is:
```json
{
'sym_variables': [('x1', 'hours worked by George'), ('x2', 'hours worked by Dale')],
'objective_function': '7*x1 + 7*x2',
'constraints': [
    '5*x1 + 3*x2 >= 14',
    '15*x1 + 9*x2 >= 14',
    'x1 - 7*x2 >= 0',
    '5*x1 + 3*x2 <= 60',
    '15*x1 + 9*x2 <= 64'
]
}
```

## 6: Gurobi Code
Now, let's implement this in Gurobi:
```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name="hours_worked_by_George", lb=0)  # hours worked by George
    x2 = model.addVar(name="hours_worked_by_Dale", lb=0)   # hours worked by Dale

    # Objective function: minimize 7*x1 + 7*x2
    model.setObjective(7*x1 + 7*x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(5*x1 + 3*x2 >= 14, name="paperwork_rating")  # paperwork competence rating >= 14
    model.addConstr(15*x1 + 9*x2 >= 14, name="computer_rating")  # computer competence rating >= 14
    model.addConstr(x1 - 7*x2 >= 0, name="george_dale_hours")  # 1*x1 - 7*x2 >= 0
    model.addConstr(5*x1 + 3*x2 <= 60, name="paperwork_upper_bound")  # paperwork upper bound
    model.addConstr(15*x1 + 9*x2 <= 64, name="computer_upper_bound")  # computer upper bound

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by George: {x1.varValue}")
        print(f"Hours worked by Dale: {x2.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```