To solve the optimization problem described, we will use the Gurobi Python interface. The problem involves minimizing an objective function that is a linear combination of hours worked by three individuals (Dale, Peggy, and Bill) subject to various constraints related to their competence ratings, work quality ratings, and dollar costs per hour.

First, let's outline the key components:
- **Decision Variables**: Hours worked by Dale (`x0`), Peggy (`x1`), and Bill (`x2`).
- **Objective Function**: Minimize `1*x0 + 3*x1 + 6*x2`.
- **Constraints**:
  - Competence ratings constraints.
  - Work quality ratings constraints.
  - Dollar cost per hour constraints.
  - Additional linear constraints.

Here is the Gurobi code that models and solves this problem:

```python
from gurobipy import *

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

# Define decision variables
x0 = m.addVar(lb=0, name="hours_worked_by_Dale")
x1 = m.addVar(lb=0, name="hours_worked_by_Peggy")
x2 = m.addVar(lb=0, name="hours_worked_by_Bill")

# Objective function
m.setObjective(1*x0 + 3*x1 + 6*x2, GRB.MINIMIZE)

# Constraints
# Paperwork competence rating constraints
m.addConstr(12*x1 + 11*x2 >= 24)  # Total combined paperwork competence rating from Peggy and Bill
m.addConstr(20*x0 + 12*x1 >= 36)  # Total combined paperwork competence rating from Dale and Peggy
m.addConstr(20*x0 + 12*x1 + 11*x2 >= 36)  # Total combined paperwork competence rating from all

# Work quality rating constraints
m.addConstr(13*x0 + 18*x2 >= 15)  # Total combined work quality rating from Dale and Bill
m.addConstr(15*x1 + 18*x2 >= 33)  # Total combined work quality rating from Peggy and Bill
m.addConstr((13*x0 + 15*x1 + 18*x2) >= 23)  # Total combined work quality rating from all

# Dollar cost per hour constraints
m.addConstr(10*x1 + 15*x2 >= 32)  # Total combined dollar cost per hour from Peggy and Bill
m.addConstr(20*x0 + 10*x1 >= 23)  # Total combined dollar cost per hour from Dale and Peggy
m.addConstr((20*x0 + 10*x1 + 15*x2) >= 24)  # Total combined dollar cost per hour from all

# Additional constraints
m.addConstr(-10*x1 + 10*x2 >= 0)
m.addConstr(13*x0 + 15*x1 <= 103)  # Work quality rating from Dale and Peggy
m.addConstr((13*x0 + 18*x2) <= 66)  # Work quality rating from Dale and Bill
m.addConstr((13*x0 + 15*x1 + 18*x2) <= 115)  # Total combined work quality rating from all
m.addConstr(10*x1 + 15*x2 <= 95)  # Dollar cost per hour from Peggy and Bill
m.addConstr((20*x0 + 15*x2) <= 42)  # Dollar cost per hour from Dale and Bill

# Solve the model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found. Hours worked by Dale: {x0.x}, Peggy: {x1.x}, Bill: {x2.x}")
else:
    print("No optimal solution found.")
```