To solve the optimization problem described, we will use the Gurobi Python API. The problem involves maximizing an objective function that depends on the hours worked by two individuals, Paul and Dale, subject to several constraints related to their paperwork competence ratings and dollar costs per hour.

The objective function to be maximized is: 3.56 * (hours worked by Paul) + 9.21 * (hours worked by Dale).

There are several constraints:

1. The total combined paperwork competence rating from hours worked by Paul and Dale must be at least 21.
2. The total combined dollar cost per hour from hours worked by Paul and Dale must be at least 12.
3. Eight times the number of hours worked by Paul, minus five times the number of hours worked by Dale, must be at least zero.
4. The total combined paperwork competence rating from hours worked by Paul and Dale must not exceed 38.
5. The total combined dollar cost per hour from hours worked by Paul and Dale must not exceed 21.

Given that both variables (hours worked by Paul and hours worked by Dale) can take non-integer values, we will model them as continuous variables in Gurobi.

Here's the reasoning behind the code:

- We import the necessary modules.
- Create a Gurobi model.
- Define the decision variables: hours worked by Paul (`x0`) and hours worked by Dale (`x1`).
- Set up the objective function to maximize.
- Add constraints based on the given conditions.

```python
from gurobipy import *

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

# Define decision variables
x0 = m.addVar(lb=0, name="hours_worked_by_Paul", vtype=GRB.CONTINUOUS)
x1 = m.addVar(lb=0, name="hours_worked_by_Dale", vtype=GRB.CONTINUOUS)

# Objective function: Maximize 3.56*x0 + 9.21*x1
m.setObjective(3.56*x0 + 9.21*x1, GRB.MAXIMIZE)

# Constraints
# 1. Total paperwork competence rating >= 21
m.addConstr(0.44*x0 + 0.93*x1 >= 21, name="paperwork_competence_min")

# 2. Total dollar cost per hour >= 12
m.addConstr(0.47*x0 + 0.89*x1 >= 12, name="dollar_cost_per_hour_min")

# 3. 8*x0 - 5*x1 >= 0
m.addConstr(8*x0 - 5*x1 >= 0, name="hours_constraint")

# 4 & 5. Total paperwork competence rating and dollar cost per hour have upper bounds
m.addConstr(0.44*x0 + 0.93*x1 <= 38, name="paperwork_competence_max")
m.addConstr(0.47*x0 + 0.89*x1 <= 21, name="dollar_cost_per_hour_max")

# Optimize model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Paul: {x0.x}")
    print(f"Hours worked by Dale: {x1.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```