## Problem Description and Formulation

The problem is an optimization problem where we need to maximize the objective function:

\[ 8.02 \times \text{hours worked by Laura} + 3.31 \times \text{hours worked by Ringo} \]

subject to several constraints.

### Variables
- \(L\): hours worked by Laura
- \(R\): hours worked by Ringo

### Constraints
1. \(12L + 1R \geq 68\)
2. \(13L + 17R \geq 44\)
3. \(16L + 16R \geq 38\)
4. \(-5L + 2R \geq 0\)
5. \(12L + 1R \leq 151\)
6. \(13L + 17R \leq 102\)
7. \(16L + 16R \leq 187\)

And the individual constraints:
- Laura's likelihood to quit index is 12.
- Laura's paperwork competence rating is 13.
- Laura's work quality rating is 16.
- Ringo has a likelihood to quit index of 1.
- Ringo has a paperwork competence rating of 17.
- Ringo's work quality rating is 16.

These individual constraints are already incorporated into the problem through the coefficients.

## Gurobi Code Formulation

```python
import gurobipy as gp

# Create a new model
model = gp.Model("optimization_problem")

# Define variables
L = model.addVar(name="hours_worked_by_Laura", lb=0)  # Assuming hours cannot be negative
R = model.addVar(name="hours_worked_by_Ringo", lb=0)  # Assuming hours cannot be negative

# Objective function
model.setObjective(8.02 * L + 3.31 * R, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(12 * L + 1 * R >= 68, name="likelihood_to_quit")
model.addConstr(13 * L + 17 * R >= 44, name="paperwork_competence")
model.addConstr(16 * L + 16 * R >= 38, name="work_quality")
model.addConstr(-5 * L + 2 * R >= 0, name="hours_tradeoff")
model.addConstr(12 * L + 1 * R <= 151, name="likelihood_to_quit_upper")
model.addConstr(13 * L + 17 * R <= 102, name="paperwork_competence_upper")
model.addConstr(16 * L + 16 * R <= 187, name="work_quality_upper")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Hours worked by Laura: {L.varValue}")
    print(f"Hours worked by Ringo: {R.varValue}")
    print(f"Objective: {model.objVal}")
else:
    print("No optimal solution found.")
```