To solve the given optimization problem using Gurobi, we need to formulate it as a linear programming (LP) model. The objective is to minimize the total cost, which is calculated as 6.93 times the hours worked by Dale plus 5.9 times the hours worked by Peggy.

Given variables:
- `x0`: Hours worked by Dale
- `x1`: Hours worked by Peggy

Objective function: Minimize `6.93*x0 + 5.9*x1`

Constraints based on the provided information:

1. Likelihood to quit index for Dale and Peggy: 
   - For Dale: `8*x0`
   - For Peggy: `8*x1`
   - Combined minimum: `8*x0 + 8*x1 >= 44`
   - Combined maximum: `8*x0 + 8*x1 <= 62`

2. Organization score for Dale and Peggy:
   - For Dale: `1*x0`
   - For Peggy: `3*x1`
   - Combined minimum: `1*x0 + 3*x1 >= 101`
   - Combined maximum: `1*x0 + 3*x1 <= 233`

3. Productivity rating for Dale and Peggy:
   - For Dale: `12*x0`
   - For Peggy: `13*x1`
   - Combined minimum: `12*x0 + 13*x1 >= 86`
   - Combined maximum: `12*x0 + 13*x1 <= 132`

4. Additional constraint: `4*x0 - 8*x1 >= 0`

Since both `x0` and `x1` can be non-integer (continuous), we don't need to specify them as integer variables.

Here's the Gurobi code that represents this optimization problem:

```python
from gurobipy import *

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

# Define variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Dale")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="hours_worked_by_Peggy")

# Objective function: Minimize 6.93*x0 + 5.9*x1
m.setObjective(6.93*x0 + 5.9*x1, GRB.MINIMIZE)

# Constraints
m.addConstr(8*x0 + 8*x1 >= 44, "Combined_likelihood_to_quit_index_minimum")
m.addConstr(8*x0 + 8*x1 <= 62, "Combined_likelihood_to_quit_index_maximum")

m.addConstr(x0 + 3*x1 >= 101, "Combined_organization_score_minimum")
m.addConstr(x0 + 3*x1 <= 233, "Combined_organization_score_maximum")

m.addConstr(12*x0 + 13*x1 >= 86, "Combined_productivity_rating_minimum")
m.addConstr(12*x0 + 13*x1 <= 132, "Combined_productivity_rating_maximum")

m.addConstr(4*x0 - 8*x1 >= 0, "Additional_constraint")

# Optimize model
m.optimize()

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

```