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

### Symbolic Representation

Let's denote:
- $x_1$ as 'hours worked by Paul',
- $x_2$ as 'hours worked by Dale'.

The objective function to maximize is: $3.56x_1 + 9.21x_2$

Constraints:
1. Total combined paperwork competence rating: $0.44x_1 + 0.93x_2 \geq 21$
2. Total combined dollar cost per hour: $0.47x_1 + 0.89x_2 \geq 12$
3. Linear constraint: $8x_1 - 5x_2 \geq 0$
4. Maximum total paperwork competence rating: $0.44x_1 + 0.93x_2 \leq 38$
5. Maximum total dollar cost per hour: $0.47x_1 + 0.89x_2 \leq 21$

### JSON Representation of the Problem

```json
{
    'sym_variables': [('x1', 'hours worked by Paul'), ('x2', 'hours worked by Dale')],
    'objective_function': '3.56*x1 + 9.21*x2',
    'constraints': [
        '0.44*x1 + 0.93*x2 >= 21',
        '0.47*x1 + 0.89*x2 >= 12',
        '8*x1 - 5*x2 >= 0',
        '0.44*x1 + 0.93*x2 <= 38',
        '0.47*x1 + 0.89*x2 <= 21'
    ]
}
```

### Gurobi Code

To solve this problem using Gurobi, we'll write the following Python code:

```python
from gurobipy import *

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

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

# Set the objective function
m.setObjective(3.56*x1 + 9.21*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(0.44*x1 + 0.93*x2 >= 21, "paperwork_competence_rating")
m.addConstr(0.47*x1 + 0.89*x2 >= 12, "dollar_cost_per_hour_min")
m.addConstr(8*x1 - 5*x2 >= 0, "linear_constraint")
m.addConstr(0.44*x1 + 0.93*x2 <= 38, "max_paperwork_competence_rating")
m.addConstr(0.47*x1 + 0.89*x2 <= 21, "max_dollar_cost_per_hour")

# Optimize the model
m.optimize()

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