## Problem Description and Formulation

The problem requires minimizing the objective function: $2.71 \times \text{hours worked by Bobby} + 4.52 \times \text{hours worked by Dale}$, subject to several constraints.

### Variables
- $x_0$: hours worked by Bobby
- $x_1$: hours worked by Dale

### Resources/Attributes
- $r_0$: work quality rating
  - Bobby's rating: 2
  - Dale's rating: 6
  - Upper bound: 26
- $r_1$: productivity rating
  - Bobby's rating: 7
  - Dale's rating: 2
  - Upper bound: 36

### Constraints
1. $2x_0 + 6x_1 \geq 13$ (total combined work quality rating $\geq 13$)
2. $7x_0 + 2x_1 \geq 9$ (total combined productivity rating $\geq 9$)
3. $-7x_0 + 5x_1 \geq 0$
4. $2x_0 + 6x_1 \leq 25$ (total combined work quality rating $\leq 25$)
5. $7x_0 + 2x_1 \leq 20$ (total combined productivity rating $\leq 20$)

## Gurobi Code

```python
import gurobipy as gp

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

# Define variables
hours_worked_by_Bobby = m.addVar(name="hours_worked_by_Bobby", lb=0)  # Assuming hours cannot be negative
hours_worked_by_Dale = m.addVar(name="hours_worked_by_Dale", lb=0)  # Assuming hours cannot be negative

# Objective function
m.setObjective(2.71 * hours_worked_by_Bobby + 4.52 * hours_worked_by_Dale, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(2 * hours_worked_by_Bobby + 6 * hours_worked_by_Dale >= 13, name="work_quality_rating_constraint")
m.addConstr(7 * hours_worked_by_Bobby + 2 * hours_worked_by_Dale >= 9, name="productivity_rating_constraint")
m.addConstr(-7 * hours_worked_by_Bobby + 5 * hours_worked_by_Dale >= 0, name="productivity_work_constraint")
m.addConstr(2 * hours_worked_by_Bobby + 6 * hours_worked_by_Dale <= 25, name="work_quality_upper_bound_constraint")
m.addConstr(7 * hours_worked_by_Bobby + 2 * hours_worked_by_Dale <= 20, name="productivity_upper_bound_constraint")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal hours worked by Bobby: {hours_worked_by_Bobby.varValue}")
    print(f"Optimal hours worked by Dale: {hours_worked_by_Dale.varValue}")
    print(f"Objective value: {m.objVal}")
else:
    print("The model is infeasible.")
```