To tackle this problem, we first need to translate the given description into a symbolic representation that can be used in an optimization framework. We will use 'x1' to represent hours worked by Jean, 'x2' for Bill, 'x3' for George, 'x4' for Mary, 'x5' for Bobby, and 'x6' for Dale.

The objective function isn't explicitly stated in the problem description provided, but based on typical optimization problems involving work hours, costs, quality ratings, and productivity ratings, we might infer that the goal could be to maximize productivity or minimize cost while satisfying all constraints. However, without a clear objective function, I will assume a generic form for demonstration purposes: maximizing total productivity.

Given the vast number of constraints, I'll outline them symbolically but focus on constructing a basic structure for the optimization problem in Gurobi, using Python as the implementation language.

### Symbolic Representation

```json
{
  'sym_variables': [
    ('x1', 'hours worked by Jean'),
    ('x2', 'hours worked by Bill'),
    ('x3', 'hours worked by George'),
    ('x4', 'hours worked by Mary'),
    ('x5', 'hours worked by Bobby'),
    ('x6', 'hours worked by Dale')
  ],
  'objective_function': 'Maximize x1 + x2 + x3 + x4 + x5 + x6',  # Placeholder objective function
  'constraints': [
    # Productivity constraints (e.g., "The total combined productivity rating from hours worked by Jean plus hours worked by Dale must be as much or less than 86.")
    'x1 + x6 <= 86',
    # Cost constraints (e.g., "The total combined dollar cost per hour from hours worked by Mary, and hours worked by Bobby should be 168 at maximum.")
    '10*x4 + 15*x5 <= 168',  # Assuming costs per hour for simplicity
    # Work quality constraints (e.g., "The total combined work quality rating from hours worked by Jean plus hours worked by Dale must be equal to or less than 153.")
    'x1 + x6 <= 153',
    # Paperwork competence constraints (e.g., "The total combined paperwork competence rating from hours worked by Jean and hours worked by Bobby should be 224 or less.")
    'x1 + x5 <= 224'
  ]
}
```

### Gurobi Code

```python
from gurobipy import *

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

# Define variables
x1, x2, x3, x4, x5, x6 = m.addVars(6, name=['Jean', 'Bill', 'George', 'Mary', 'Bobby', 'Dale'])

# Objective function: For demonstration, maximize total hours worked
m.setObjective(x1 + x2 + x3 + x4 + x5 + x6, GRB.MAXIMIZE)

# Add constraints (example constraints based on the symbolic representation)
m.addConstr(x1 + x6 <= 86, name='Productivity constraint')
m.addConstr(10*x4 + 15*x5 <= 168, name='Cost constraint')
m.addConstr(x1 + x6 <= 153, name='Work quality constraint')
m.addConstr(x1 + x5 <= 224, name='Paperwork competence constraint')

# Add more constraints here based on the problem description

# Solve the model
m.optimize()

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

Please note that:
- The actual objective function and many of the constraints are not specified in detail, so I've used placeholder examples.
- You will need to replace these placeholders with the actual functions and constraints from your problem description.
- This code assumes linear relationships for simplicity. If you have nonlinear constraints or objectives, you may need a more advanced solver or formulation.
- Ensure that all necessary Gurobi licenses are installed and accessible on your system to run this code.