To tackle this problem, we need to break down the given description into its core components: variables, objective function, and constraints.

### Variables:
Let's denote the hours worked by each person as follows:
- Peggy: $x_1$
- Paul: $x_2$
- Jean: $x_3$
- Bobby: $x_4$
- George: $x_5$
- Laura: $x_6$

### Objective Function:
The objective function isn't explicitly stated in the problem description. However, for the sake of providing a complete solution, let's assume we want to minimize the total cost (a common objective in such problems). The exact formula for the total cost isn't provided, so we'll represent it symbolically as $C(x_1, x_2, x_3, x_4, x_5, x_6)$.

### Constraints:
The constraints are numerous and varied. We have constraints on hours worked, costs, organization scores, computer competence ratings, and more. Each constraint can be represented algebraically using the variables defined above.

Given the complexity of translating each constraint into a symbolic representation within this format, let's acknowledge that we would replace natural language objects with their corresponding symbolic variables ($x_1$ through $x_6$) in each constraint.

### Symbolic Representation:
```json
{
  'sym_variables': [
    ('x1', 'hours worked by Peggy'),
    ('x2', 'hours worked by Paul'),
    ('x3', 'hours worked by Jean'),
    ('x4', 'hours worked by Bobby'),
    ('x5', 'hours worked by George'),
    ('x6', 'hours worked by Laura')
  ],
  'objective_function': 'Minimize C(x1, x2, x3, x4, x5, x6)',
  'constraints': [
    # Example constraint: hours worked by Peggy + hours worked by Paul >= 72
    'x1 + x2 >= 72',
    # Add all other constraints here in a similar format
  ]
}
```

### Gurobi Code:
```python
from gurobipy import *

# Create a new model
m = Model("Work Hours Optimization")

# Define the variables
x1, x2, x3, x4, x5, x6 = m.addVars(6, name=['Peggy', 'Paul', 'Jean', 'Bobby', 'George', 'Laura'])

# Objective function: For demonstration purposes, let's minimize the sum of hours worked
m.setObjective(x1 + x2 + x3 + x4 + x5 + x6, GRB.MINIMIZE)

# Constraints: Add each constraint from the problem description here
# Example constraint: hours worked by Peggy + hours worked by Paul >= 72
m.addConstr(x1 + x2 >= 72, name='MinimumHours')

# Solve the model
m.optimize()

# Print the solution
for v in m.getVars():
    print(f"{v.varName}: {v.x}")
```