To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables, an objective function, and constraints using algebraic terms.

Let's denote:
- $x_1$ as 'hours worked by John'
- $x_2$ as 'hours worked by Paul'

The objective function is to maximize: $8x_1 + 5x_2$

Constraints are as follows:
1. Total combined paperwork competence rating: $x_1 + 22x_2 \geq 57$
2. Total combined organization score: $5x_1 + 28x_2 \geq 31$
3. Total combined dollar cost per hour: $11x_1 + 21x_2 \geq 43$
4. Linear constraint: $-3x_1 + 10x_2 \geq 0$
5. Upper bound for total paperwork competence rating: $x_1 + 22x_2 \leq 86$
6. Upper bound for total organization score: $5x_1 + 28x_2 \leq 124$
7. Upper bound for total dollar cost per hour: $11x_1 + 21x_2 \leq 60$

Given the symbolic representation, we can now express this in JSON format as requested:

```json
{
    'sym_variables': [('x1', 'hours worked by John'), ('x2', 'hours worked by Paul')],
    'objective_function': '8*x1 + 5*x2',
    'constraints': [
        'x1 + 22*x2 >= 57',
        '5*x1 + 28*x2 >= 31',
        '11*x1 + 21*x2 >= 43',
        '-3*x1 + 10*x2 >= 0',
        'x1 + 22*x2 <= 86',
        '5*x1 + 28*x2 <= 124',
        '11*x1 + 21*x2 <= 60'
    ]
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, name="hours_worked_by_John")
x2 = m.addVar(lb=0, name="hours_worked_by_Paul")

# Set the objective function
m.setObjective(8*x1 + 5*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + 22*x2 >= 57, "paperwork_competence_rating")
m.addConstr(5*x1 + 28*x2 >= 31, "organization_score")
m.addConstr(11*x1 + 21*x2 >= 43, "dollar_cost_per_hour")
m.addConstr(-3*x1 + 10*x2 >= 0, "linear_constraint")
m.addConstr(x1 + 22*x2 <= 86, "upper_bound_paperwork")
m.addConstr(5*x1 + 28*x2 <= 124, "upper_bound_organization")
m.addConstr(11*x1 + 21*x2 <= 60, "upper_bound_dollar_cost")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hours worked by John: {x1.x}")
    print(f"Hours worked by Paul: {x2.x}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found")
```