To solve the optimization problem described, we'll use the Gurobi Python library. The goal is to maximize the objective function `7*x0 + 3*x1 + 3*x2`, where `x0`, `x1`, and `x2` represent the hours worked by Peggy, Paul, and Hank, respectively.

Given constraints:
- Productivity ratings: Peggy (1), Paul (1), Hank (8)
- Paperwork competence ratings: Peggy (3), Paul (7), Hank (2)
- Minimum total productivity rating of 12
- Various constraints on combined paperwork competence ratings and productivity ratings

First, let's clarify the variables and their types:
- `x0` (Peggy): integer
- `x1` (Paul): continuous
- `x2` (Hank): integer

We'll define these in Gurobi accordingly.

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Peggy")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Paul")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Hank")

# Objective function: Maximize 7*x0 + 3*x1 + 3*x2
m.setObjective(7*x0 + 3*x1 + 3*x2, GRB.MAXIMIZE)

# Constraints:
# Minimum total productivity rating of 12
m.addConstr(x0 + x1 + 8*x2 >= 12, name="min_productivity")

# Combined paperwork competence ratings constraints
m.addConstr(3*x0 + 2*x2 <= 27, name="paperwork_Peggy_Hank")
m.addConstr(7*x1 + 2*x2 <= 27, name="paperwork_Paul_Hank")
m.addConstr(3*x0 + 7*x1 <= 34, name="paperwork_Peggy_Paul")
m.addConstr(3*x0 + 7*x1 + 2*x2 <= 34, name="paperwork_all")

# Combined productivity ratings constraints
m.addConstr(x1 + 8*x2 <= 29, name="productivity_Paul_Hank")
m.addConstr(x0 + x1 <= 33, name="productivity_Peggy_Paul")
m.addConstr(x0 + x1 + 8*x2 <= 33, name="productivity_all")

# Optimize model
m.optimize()

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Peggy")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Paul")
x2 = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Hank")

# Objective function: Maximize 7*x0 + 3*x1 + 3*x2
m.setObjective(7*x0 + 3*x1 + 3*x2, GRB.MAXIMIZE)

# Constraints:
# Minimum total productivity rating of 12
m.addConstr(x0 + x1 + 8*x2 >= 12, name="min_productivity")

# Combined paperwork competence ratings constraints
m.addConstr(3*x0 + 2*x2 <= 27, name="paperwork_Peggy_Hank")
m.addConstr(7*x1 + 2*x2 <= 27, name="paperwork_Paul_Hank")
m.addConstr(3*x0 + 7*x1 <= 34, name="paperwork_Peggy_Paul")
m.addConstr(3*x0 + 7*x1 + 2*x2 <= 34, name="paperwork_all")

# Combined productivity ratings constraints
m.addConstr(x1 + 8*x2 <= 29, name="productivity_Paul_Hank")
m.addConstr(x0 + x1 <= 33, name="productivity_Peggy_Paul")
m.addConstr(x0 + x1 + 8*x2 <= 33, name="productivity_all")

# Optimize model
m.optimize()
```