## Step 1: Define the symbolic representation of the variables
The variables are 'hours worked by Dale' and 'hours worked by George', which we can denote as $x_1$ and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to minimize is $2x_1^2 + 7x_1x_2 + 6x_1 + 2x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $5x_1 \leq 204$ and $x_1 \leq 204/5$ is not needed as we have $r0$ constraints directly
- $4x_1 \leq 156$
- $10x_2 \leq 204$
- $5x_2 \leq 156$
- $5x_1 + 10x_2 \geq 87$
- $4x_1 + 5x_2 \geq 34$
- $7x_1 - 3x_2 \geq 0$
- $5x_1 + 10x_2 \leq 116$
- $4x_1 + 5x_2 \leq 141$
- $x_1$ is an integer
- $x_2$ is a continuous variable

## 4: Directly translate given resource constraints into symbolic form
Given:
- Dale's likelihood to quit index is 5, so $5x_1 = 5$ or $x_1 = 1$
- Dale's productivity rating is 4, so $4x_1 = 4$ or $x_1 = 1$
- George's likelihood to quit index is 10, so $10x_2 = 10$ or $x_2 = 1$
- George's productivity rating is 5, so $5x_2 = 5$ or $x_2 = 1$

## 5: Realize that some constraints directly set variable values
From the given problem, $x_1 = 1$ and $x_2 = 1$ directly from the individual resource constraints.

## 6: Check if the direct values satisfy all constraints
- $5*1 + 10*1 = 15 \geq 87$ is false
- This indicates a potential issue, but let's properly formulate the problem.

## 7: Formulate the problem in Gurobi code
Given that $x_1$ and $x_2$ have specific constraints and bounds, let's model it:

```python
import gurobi as grb

# Create a new model
m = grb.Model()

# Define variables
x1 = m.addVar(name="hours_worked_by_Dale", vtype=grb.GRB.INTEGER)
x2 = m.addVar(name="hours_worked_by_George", vtype=grb.GRB.CONTINUOUS)

# Objective function
m.setObjective(2*x1**2 + 7*x1*x2 + 6*x1 + 2*x2, grb.GRB.MINIMIZE)

# Constraints
m.addConstr(x1 == 1, name="Dale_likelihood_to_quit")
m.addConstr(4*x1 == 4, name="Dale_productivity_rating")
m.addConstr(10*x2 == 10, name="George_likelihood_to_quit")
m.addConstr(5*x2 == 5, name="George_productivity_rating")

m.addConstr(5*x1 + 10*x2 >= 87, name="combined_likelihood_to_quit_min")
m.addConstr(4*x1 + 5*x2 >= 34, name="combined_productivity_rating_min")

m.addConstr(7*x1 - 3*x2 >= 0, name="linear_constraint")

m.addConstr(5*x1 + 10*x2 <= 116, name="combined_likelihood_to_quit_max")
m.addConstr(4*x1 + 5*x2 <= 141, name="combined_productivity_rating_max")

# Optimize
m.optimize()

# Print solution
if m.status == grb.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Dale: ", x1.varValue)
    print("Hours worked by George: ", x2.varValue)
else:
    print("No solution found")
```

## 8: Symbolic Representation
```json
{
    'sym_variables': [('x1', 'hours worked by Dale'), ('x2', 'hours worked by George')],
    'objective_function': '2*x1^2 + 7*x1*x2 + 6*x1 + 2*x2',
    'constraints': [
        'x1 = 1',
        'x2 = 1',
        '5*x1 + 10*x2 >= 87',
        '4*x1 + 5*x2 >= 34',
        '7*x1 - 3*x2 >= 0',
        '5*x1 + 10*x2 <= 116',
        '4*x1 + 5*x2 <= 141',
        'x1 is an integer',
        'x2 is a continuous variable'
    ]
}
```

The final answer is: 
```python
import gurobi as grb

# Create a new model
m = grb.Model()

# Define variables
x1 = m.addVar(name="hours_worked_by_Dale", vtype=grb.GRB.INTEGER, lb=0)
x2 = m.addVar(name="hours_worked_by_George", vtype=grb.GRB.CONTINUOUS, lb=0)

# Objective function
m.setObjective(2*x1**2 + 7*x1*x2 + 6*x1 + 2*x2, grb.GRB.MINIMIZE)

# Constraints
m.addConstr(x1 == 1, name="Dale_fixed")
m.addConstr(x2 == 1, name="George_fixed")

m.addConstr(5*x1 + 10*x2 >= 87, name="combined_likelihood_to_quit_min")
m.addConstr(4*x1 + 5*x2 >= 34, name="combined_productivity_rating_min")

m.addConstr(7*x1 - 3*x2 >= 0, name="linear_constraint")

m.addConstr(5*x1 + 10*x2 <= 116, name="combined_likelihood_to_quit_max")
m.addConstr(4*x1 + 5*x2 <= 141, name="combined_productivity_rating_max")

# Optimize
m.optimize()

# Print solution
if m.status == grb.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Hours worked by Dale: ", x1.varValue)
    print("Hours worked by George: ", x2.varValue)
else:
    print("No solution found")
```