## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Bobby' and 'hours worked by Dale', which can be represented symbolically as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $2.71x_1 + 4.52x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $2x_1 + 6x_2 \geq 13$ (total combined work quality rating)
- $7x_1 + 2x_2 \geq 9$ (total combined productivity rating)
- $-7x_1 + 5x_2 \geq 0$
- $2x_1 + 6x_2 \leq 25$ (upper bound on total combined work quality rating)
- $7x_1 + 2x_2 \leq 20$ (upper bound on total combined productivity rating)

## 4: Consider the upper bounds for work quality and productivity ratings
Given that the work quality rating has an upper bound of 26 and the productivity rating has an upper bound of 36, we need to ensure $x_1$ and $x_2$ are such that these bounds are respected. However, the specific upper bounds for $x_1$ and $x_2$ are not directly provided but we have $r0$ and $r1$ which seem to relate to $x_0=2, x_1=6$ for $r0$ and $x_0=7, x_1=2$ for $r1$. These seem to be misinterpreted as they directly provide ratings rather than bounds for $x_1$ and $x_2$. The actual bounds or limits on $x_1$ and $x_2$ (hours worked) aren't explicitly given except that they can be fractional.

## 5: Formulate the problem in Gurobi
To solve this linear programming problem using Gurobi, we first need to install the Gurobi library if not already installed. Then, we can write the following Python code:

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="hours_worked_by_Bobby", lb=0)  # Lower bound is 0, assuming can't work negative hours
x2 = model.addVar(name="hours_worked_by_Dale", lb=0)

# Define the objective function
model.setObjective(2.71 * x1 + 4.52 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(2 * x1 + 6 * x2 >= 13, name="work_quality_rating")
model.addConstr(7 * x1 + 2 * x2 >= 9, name="productivity_rating")
model.addConstr(-7 * x1 + 5 * x2 >= 0, name="productivity_vs_quality")
model.addConstr(2 * x1 + 6 * x2 <= 25, name="max_work_quality_rating")
model.addConstr(7 * x1 + 2 * x2 <= 20, name="max_productivity_rating")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Bobby: {x1.varValue}")
    print(f"Hours worked by Dale: {x2.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```

## 6: Symbolic Representation
The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'hours worked by Bobby'), ('x2', 'hours worked by Dale')],
    'objective_function': '2.71*x1 + 4.52*x2',
    'constraints': [
        '2*x1 + 6*x2 >= 13',
        '7*x1 + 2*x2 >= 9',
        '-7*x1 + 5*x2 >= 0',
        '2*x1 + 6*x2 <= 25',
        '7*x1 + 2*x2 <= 20'
    ]
}
```

```python
import gurobi

# Create a new model
model = gurobi.Model()

# Define the variables
x1 = model.addVar(name="hours_worked_by_Bobby", lb=0)  
x2 = model.addVar(name="hours_worked_by_Dale", lb=0)

# Define the objective function
model.setObjective(2.71 * x1 + 4.52 * x2, gurobi.GRB.MINIMIZE)

# Add constraints
model.addConstr(2 * x1 + 6 * x2 >= 13, name="work_quality_rating")
model.addConstr(7 * x1 + 2 * x2 >= 9, name="productivity_rating")
model.addConstr(-7 * x1 + 5 * x2 >= 0, name="productivity_vs_quality")
model.addConstr(2 * x1 + 6 * x2 <= 25, name="max_work_quality_rating")
model.addConstr(7 * x1 + 2 * x2 <= 20, name="max_productivity_rating")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Hours worked by Bobby: {x1.varValue}")
    print(f"Hours worked by Dale: {x2.varValue}")
    print(f"Objective function value: {model.objVal}")
else:
    print("No optimal solution found.")
```