## Problem Description and Formulation

The problem requires minimizing an objective function subject to several constraints. The objective function to be minimized is:

\[ 8.6 \times \text{hours worked by Dale} \times \text{hours worked by John} + 8.47 \times (\text{hours worked by John})^2 + 3.71 \times \text{hours worked by Dale} \]

The constraints are:

1. The computer competence rating of Dale is 8.
2. The dollar cost per hour of Dale is 15.
3. The computer competence rating of John is 13.
4. The dollar cost per hour of John is 13.
5. The total combined computer competence rating from hours worked by Dale squared and hours worked by John squared must be at least 22.
6. The total combined computer competence rating from hours worked by Dale plus hours worked by John must be at least 22.
7. The total combined dollar cost per hour from hours worked by Dale plus hours worked by John must be at least 39.
8. \(2 \times \text{hours worked by Dale} - \text{hours worked by John} \geq 0\).
9. The total combined computer competence rating from hours worked by Dale squared and hours worked by John squared must be at most 79.
10. The total combined dollar cost per hour from hours worked by Dale plus hours worked by John must be at most 43.
11. The hours worked by Dale must be an integer.
12. The hours worked by John can be a non-integer.

## Gurobi Code Formulation

Given the problem description, we can formulate the Gurobi code as follows:

```python
import gurobi

def optimization_problem():
    # Create a new Gurobi model
    model = gurobi.Model()

    # Define variables
    dale_hours = model.addVar(name="dale_hours", lb=0, type=gurobi.GRB.INTEGER)
    john_hours = model.addVar(name="john_hours", lb=0)

    # Objective function
    model.setObjective(8.6 * dale_hours * john_hours + 8.47 * john_hours**2 + 3.71 * dale_hours, gurobi.GRB.MINIMIZE)

    # Constraints
    # 5. The total combined computer competence rating from hours worked by Dale squared and hours worked by John squared must be at least 22.
    model.addConstr(8**2 * dale_hours**2 + 13**2 * john_hours**2 >= 22, "computer_competence_rating_squared_min")

    # 6. The total combined computer competence rating from hours worked by Dale plus hours worked by John must be at least 22.
    model.addConstr(8 * dale_hours + 13 * john_hours >= 22, "computer_competence_rating_min")

    # 7. The total combined dollar cost per hour from hours worked by Dale plus hours worked by John must be at least 39.
    model.addConstr(15 * dale_hours + 13 * john_hours >= 39, "dollar_cost_min")

    # 8. 2 times the number of hours worked by Dale, plus -1 times the number of hours worked by John should be greater than or equal to zero.
    model.addConstr(2 * dale_hours - john_hours >= 0, "dale_john_hours_relation")

    # 9. The total combined computer competence rating from hours worked by Dale squared and hours worked by John squared should be at maximum 79.
    model.addConstr(8**2 * dale_hours**2 + 13**2 * john_hours**2 <= 79, "computer_competence_rating_squared_max")

    # 10. The total combined dollar cost per hour from hours worked by Dale plus hours worked by John must be at most 43.
    model.addConstr(15 * dale_hours + 13 * john_hours <= 43, "dollar_cost_max")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal Solution:")
        print(f"Dale's hours: {dale_hours.varValue}")
        print(f"John's hours: {john_hours.varValue}")
    else:
        print("No optimal solution found.")

optimization_problem()
```

This code defines the optimization problem using Gurobi, sets up the objective function and constraints according to the problem description, and solves the model. The solution is then printed out. Note that due to the nature of the problem and Gurobi's solver, the solution may take some time to compute or may indicate that no feasible solution exists.