## Problem Description and Formulation

The problem is an optimization problem with two variables: 'hours worked by Dale' and 'hours worked by Peggy'. The objective is to minimize the function: 6.93 * (hours worked by Dale) + 5.9 * (hours worked by Peggy).

The problem has several constraints:

1. Individual constraints for Dale and Peggy regarding their likelihood to quit index, organization score, and productivity rating.
2. Combined constraints for the total likelihood to quit index, organization score, and productivity rating.
3. A linear constraint combining hours worked by Dale and Peggy.
4. Upper and lower bounds for the combined indices.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define variables
    dale_hours = model.addVar(lb=0, name="dale_hours")  # hours worked by Dale
    peggy_hours = model.addVar(lb=0, name="peggy_hours")  # hours worked by Peggy

    # Objective function: Minimize 6.93 * dale_hours + 5.9 * peggy_hours
    model.setObjective(6.93 * dale_hours + 5.9 * peggy_hours, gurobi.GRB.MINIMIZE)

    # Constraints
    # Individual constraints (these are actually bounds on the variables, not constraints)
    # Dale's constraints
    model.addConstraint(dale_hours * 8 <= 94, name="dale_likelihood_quit")
    model.addConstraint(dale_hours * 1 <= 290, name="dale_organization_score")
    model.addConstraint(dale_hours * 12 <= 242, name="dale_productivity_rating")

    # Peggy's constraints
    model.addConstraint(peggy_hours * 8 <= 94, name="peggy_likelihood_quit")
    model.addConstraint(peggy_hours * 3 <= 290, name="peggy_organization_score")
    model.addConstraint(peggy_hours * 13 <= 242, name="peggy_productivity_rating")

    # Combined constraints
    model.addConstraint(dale_hours * 8 + peggy_hours * 8 >= 44, name="combined_likelihood_quit_min")
    model.addConstraint(dale_hours * 8 + peggy_hours * 8 <= 62, name="combined_likelihood_quit_max")

    model.addConstraint(dale_hours * 1 + peggy_hours * 3 >= 101, name="combined_organization_score_min")
    model.addConstraint(dale_hours * 1 + peggy_hours * 3 <= 233, name="combined_organization_score_max")

    model.addConstraint(dale_hours * 12 + peggy_hours * 13 >= 86, name="combined_productivity_rating_min")
    model.addConstraint(dale_hours * 12 + peggy_hours * 13 <= 132, name="combined_productivity_rating_max")

    # Linear constraint
    model.addConstraint(4 * dale_hours - 8 * peggy_hours >= 0, name="linear_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Hours worked by Dale: {dale_hours.varValue}")
        print(f"Hours worked by Peggy: {peggy_hours.varValue}")
        print(f"Objective: {model.objVal}")
    elif model.status == gurobi.GRB.INFEASIBLE:
        print("No feasible solution exists.")
    else:
        print("Optimization failed.")

solve_optimization_problem()
```