To address the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining the variables, the objective function, and the constraints using algebraic notation.

Given:
- Variables: hours worked by George (let's denote this as `x1`), hours worked by Dale (denoted as `x2`)
- Objective Function: Minimize `7*x1 + 7*x2`
- Constraints:
  1. Total combined paperwork competence rating from hours worked by George and Dale ≥ 14
     - Symbolic Representation: `5*x1 + 3*x2 ≥ 14`
  2. Same as constraint 1, reinforcing the minimum requirement.
  3. Total combined computer competence rating from hours worked by George and Dale ≥ 14
     - Symbolic Representation: `15*x1 + 9*x2 ≥ 14`
  4. Same as constraint 3, emphasizing the minimum requirement for computer competence.
  5. `x1 - 7*x2 ≥ 0`
  6. Total combined paperwork competence rating from hours worked by George and Dale ≤ 45
     - Symbolic Representation: `5*x1 + 3*x2 ≤ 45`
  7. Total combined computer competence rating from hours worked by George and Dale ≤ 50
     - Symbolic Representation: `15*x1 + 9*x2 ≤ 50`

Symbolic Representation of the Problem:
```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 <= 45',
    '15*x1 + 9*x2 <= 50'
  ]
}
```

Now, let's implement this problem using Gurobi in Python. We will use the `gurobipy` library to formulate and solve the linear programming problem.

```python
from gurobipy import *

# Create a new model
m = Model("Optimization_Problem")

# Define variables
x1 = m.addVar(lb=0, name="hours_worked_by_George")
x2 = m.addVar(lb=0, name="hours_worked_by_Dale")

# Set the objective function
m.setObjective(7*x1 + 7*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(5*x1 + 3*x2 >= 14, "paperwork_minimum")
m.addConstr(15*x1 + 9*x2 >= 14, "computer_minimum")
m.addConstr(x1 - 7*x2 >= 0, "george_dale_hours")
m.addConstr(5*x1 + 3*x2 <= 45, "paperwork_maximum")
m.addConstr(15*x1 + 9*x2 <= 50, "computer_maximum")

# Optimize the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by George: {x1.x}")
    print(f"Hours worked by Dale: {x2.x}")
else:
    print("No optimal solution found.")
```