To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints.

Let's denote:
- $x_1$ as the hours worked by Peggy,
- $x_2$ as the hours worked by Bill.

The objective function is to minimize: $2x_1 + 3x_2$

Given the attributes and resources:
- Dollar cost per hour for Peggy is 6, for Bill is 6.
- Paperwork competence rating for Peggy is 14, for Bill is 6.
- Computer competence rating for Peggy is 9, for Bill is 15.

The constraints are:
1. Total combined dollar cost per hour from hours worked by Peggy and Bill must be at least 63: $6x_1 + 6x_2 \geq 63$
2. The same as constraint 1 but ensuring it's explicitly stated to be "equal to or greater than 63": $6x_1 + 6x_2 \geq 63$
3. Total combined paperwork competence rating from hours worked by Peggy and Bill must be at least 34: $14x_1 + 6x_2 \geq 34$
4. The same as constraint 3, emphasizing "at least 34": $14x_1 + 6x_2 \geq 34$
5. Total combined computer competence rating from hours worked by Peggy and Bill must be at least 50: $9x_1 + 15x_2 \geq 50$
6. The same as constraint 5, emphasizing "at least 50": $9x_1 + 15x_2 \geq 50$
7. $5x_1 - 9x_2 \geq 0$
8. Total combined dollar cost per hour from hours worked by Peggy and Bill must be at most 132: $6x_1 + 6x_2 \leq 132$
9. Total combined paperwork competence rating from hours worked by Peggy and Bill has to be at most 159: $14x_1 + 6x_2 \leq 159$
10. Total combined computer competence rating from hours worked by Peggy and Bill must be at most 151: $9x_1 + 15x_2 \leq 151$

Symbolic representation:
```json
{
    'sym_variables': [('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Bill')],
    'objective_function': '2*x1 + 3*x2',
    'constraints': [
        '6*x1 + 6*x2 >= 63',
        '14*x1 + 6*x2 >= 34',
        '9*x1 + 15*x2 >= 50',
        '5*x1 - 9*x2 >= 0',
        '6*x1 + 6*x2 <= 132',
        '14*x1 + 6*x2 <= 159',
        '9*x1 + 15*x2 <= 151'
    ]
}
```

Given the nature of the constraints and the objective function, we can now proceed to implement this problem in Gurobi. Since the problem involves linear constraints and a linear objective function, it's a Linear Programming (LP) problem.

```python
from gurobipy import *

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

# Create variables
x1 = m.addVar(lb=0, name="hours_worked_by_Peggy")
x2 = m.addVar(lb=0, name="hours_worked_by_Bill")

# Set the objective function
m.setObjective(2*x1 + 3*x2, GRB.MINIMIZE)

# Add constraints
m.addConstr(6*x1 + 6*x2 >= 63, "dollar_cost_min")
m.addConstr(14*x1 + 6*x2 >= 34, "paperwork_rating_min")
m.addConstr(9*x1 + 15*x2 >= 50, "computer_rating_min")
m.addConstr(5*x1 - 9*x2 >= 0, "mixed_constraint")
m.addConstr(6*x1 + 6*x2 <= 132, "dollar_cost_max")
m.addConstr(14*x1 + 6*x2 <= 159, "paperwork_rating_max")
m.addConstr(9*x1 + 15*x2 <= 151, "computer_rating_max")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by Peggy: {x1.x}")
    print(f"Hours worked by Bill: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```