To solve this optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining the variables, objective function, and constraints in terms of these symbols.

### Symbolic Representation:

- Let $x_0$ represent 'hours worked by Dale'.
- Let $x_1$ represent 'hours worked by Bill'.

The objective function is to minimize $1 \cdot x_0 + 1 \cdot x_1$, which simplifies to $x_0 + x_1$.

The constraints can be summarized as follows:
1. Work quality rating: $25x_0 + 21x_1 \geq 43$
2. Organization score: $20x_0 + x_1 \geq 36$
3. Paperwork competence rating: $11x_0 + 27x_1 \geq 47$
4. Linear inequality constraint: $-8x_0 + 2x_1 \geq 0$
5. Upper bound on combined work quality rating: $25x_0 + 21x_1 \leq 80$
6. Upper bound on combined organization score: $20x_0 + x_1 \leq 105$
7. Upper bound on combined paperwork competence rating: $11x_0 + 27x_1 \leq 65$

### Symbolic Representation in JSON Format:
```json
{
    'sym_variables': [('x0', 'hours worked by Dale'), ('x1', 'hours worked by Bill')],
    'objective_function': 'x0 + x1',
    'constraints': [
        '25*x0 + 21*x1 >= 43',
        '20*x0 + x1 >= 36',
        '11*x0 + 27*x1 >= 47',
        '-8*x0 + 2*x1 >= 0',
        '25*x0 + 21*x1 <= 80',
        '20*x0 + x1 <= 105',
        '11*x0 + 27*x1 <= 65'
    ]
}
```

### Gurobi Code:
```python
from gurobipy import *

# Create a model
m = Model("Optimization_Problem")

# Define variables
x0 = m.addVar(name='hours_worked_by_Dale', lb=0)
x1 = m.addVar(name='hours_worked_by_Bill', lb=0)

# Set objective function
m.setObjective(x0 + x1, GRB.MINIMIZE)

# Add constraints
m.addConstr(25*x0 + 21*x1 >= 43, name='work_quality_rating')
m.addConstr(20*x0 + x1 >= 36, name='organization_score')
m.addConstr(11*x0 + 27*x1 >= 47, name='paperwork_competence_rating')
m.addConstr(-8*x0 + 2*x1 >= 0, name='linear_inequality_constraint')
m.addConstr(25*x0 + 21*x1 <= 80, name='upper_bound_work_quality_rating')
m.addConstr(20*x0 + x1 <= 105, name='upper_bound_organization_score')
m.addConstr(11*x0 + 27*x1 <= 65, name='upper_bound_paperwork_competence_rating')

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print('Optimal solution found:')
    print(f'Hours worked by Dale: {x0.x}')
    print(f'Hours worked by Bill: {x1.x}')
else:
    print('No optimal solution found')
```