To solve the given optimization problem using Gurobi, we first need to translate the natural language description into a mathematical formulation that can be represented in code. The objective function and constraints are described as follows:

- Objective Function: Minimize \(8.6 \times \text{hours worked by Dale} \times \text{hours worked by John} + 8.47 \times (\text{hours worked by John})^2 + 3.71 \times \text{hours worked by Dale}\)
- Constraints:
  1. Computer competence rating for Dale: \(8\)
  2. Dollar cost per hour for Dale: \(15\)
  3. Computer competence rating for John: \(13\)
  4. Dollar cost per hour for John: \(13\)
  5. Minimum total combined computer competence rating from hours worked by Dale and John squared: \((8 \times \text{hours worked by Dale})^2 + (13 \times \text{hours worked by John})^2 \geq 22\)
  6. Minimum total combined computer competence rating from hours worked by Dale and John: \(8 \times \text{hours worked by Dale} + 13 \times \text{hours worked by John} \geq 22\)
  7. Minimum total combined dollar cost per hour from hours worked by Dale and John: \(15 \times \text{hours worked by Dale} + 13 \times \text{hours worked by John} \geq 39\)
  8. Same as constraint 7, emphasizing it must be at least 39.
  9. Constraint on hours worked by Dale and John: \(2 \times \text{hours worked by Dale} - 1 \times \text{hours worked by John} \geq 0\)
  10. Maximum total combined computer competence rating from hours worked by Dale squared and John squared: \((8 \times \text{hours worked by Dale})^2 + (13 \times \text{hours worked by John})^2 \leq 79\)
  11. Maximum total combined dollar cost per hour from hours worked by Dale and John: \(15 \times \text{hours worked by Dale} + 13 \times \text{hours worked by John} \leq 43\)
  12. Hours worked by Dale must be an integer.
  13. Hours worked by John may be a non-integer.

Given these constraints, we can model this problem using Gurobi as follows:

```python
from gurobipy import *

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

# Define the variables
dale_hours = m.addVar(vtype=GRB.INTEGER, name="hours_worked_by_Dale")
john_hours = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_John")

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

# Constraints
m.addConstr((8 * dale_hours)**2 + (13 * john_hours)**2 >= 22, name="min_total_comp_rating_squared")
m.addConstr(8 * dale_hours + 13 * john_hours >= 22, name="min_total_comp_rating")
m.addConstr(15 * dale_hours + 13 * john_hours >= 39, name="min_total_dollar_cost_per_hour_1")
m.addConstr(15 * dale_hours + 13 * john_hours >= 39, name="min_total_dollar_cost_per_hour_2")
m.addConstr(2 * dale_hours - john_hours >= 0, name="hours_worked_constraint")
m.addConstr((8 * dale_hours)**2 + (13 * john_hours)**2 <= 79, name="max_total_comp_rating_squared")
m.addConstr(15 * dale_hours + 13 * john_hours <= 43, name="max_total_dollar_cost_per_hour")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Hours worked by Dale:", dale_hours.x)
    print("Hours worked by John:", john_hours.x)
else:
    print("No optimal solution found. Status:", m.status)

```

This code sets up the optimization problem according to the given objective function and constraints, then solves it using Gurobi's solver. The results include the optimal number of hours worked by Dale and John that minimize the objective function while satisfying all constraints.