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

### Symbolic Representation of the Problem:

- **Variables:**
  - Let \(x_1\) represent 'hours worked by Peggy'.
  - Let \(x_2\) represent 'hours worked by Bill'.

- **Objective Function:**
  The objective is to maximize \(3.66x_1 + 2.91x_2\).

- **Constraints:**
  1. \(0.81x_1 + 21.75x_2 \geq 69\) (Total combined computer competence rating from hours worked by Peggy and Bill must be 69 or more).
  2. \(2x_1 - 3x_2 \geq 0\) (2 times the number of hours worked by Peggy, plus -3 times the number of hours worked by Bill must be no less than zero).
  3. \(0.81x_1 + 21.75x_2 \leq 168\) (Total combined computer competence rating from hours worked by Peggy and Bill should be less than or equal to 168).
  Note: The constraint about the total being equal to or less than 168 is redundant with the third point, so it's not listed separately.

- **Non-Negativity Constraints:** Since hours cannot be negative, \(x_1 \geq 0\) and \(x_2 \geq 0\).

Given this setup, we can now represent our problem symbolically as:

```json
{
  'sym_variables': [('x1', 'hours worked by Peggy'), ('x2', 'hours worked by Bill')],
  'objective_function': '3.66*x1 + 2.91*x2',
  'constraints': [
    '0.81*x1 + 21.75*x2 >= 69',
    '2*x1 - 3*x2 >= 0',
    '0.81*x1 + 21.75*x2 <= 168',
    'x1 >= 0',
    'x2 >= 0'
  ]
}
```

### Gurobi Code:

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Add variables to the model
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(3.66*x1 + 2.91*x2, GRB.MAXIMIZE)

# Add constraints to the model
m.addConstr(0.81*x1 + 21.75*x2 >= 69, "combined_competence_rating_min")
m.addConstr(2*x1 - 3*x2 >= 0, "peggy_bill_hours_ratio")
m.addConstr(0.81*x1 + 21.75*x2 <= 168, "combined_competence_rating_max")

# Optimize the model
m.optimize()

# Print results
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")
```

This code defines the optimization problem as described, solves it using Gurobi, and prints out the results.