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 mathematical notation.

### Symbolic Representation:

Let's define:
- $x_1$ as the hours worked by Dale,
- $x_2$ as the hours worked by Hank.

The objective function is to maximize: $4x_1^2 + 6x_1x_2 + 7x_1$

Constraints are:
1. $4x_1 \leq 82$ (Dale's computer competence rating constraint)
2. $4x_2 \leq 82$ (Hank's computer competence rating constraint)
3. $4x_1 + 4x_2 \geq 29$ (Minimum total combined computer competence rating)
4. $-8x_1 + 6x_2 \geq 0$ (Specific linear constraint)
5. $4x_1 + 4x_2 \leq 70$ (Maximum total combined computer competence rating)

Given the problem's requirements, we don't need to enforce integer solutions for $x_1$ and $x_2$, so both can be continuous variables.

### Symbolic Representation in JSON Format:

```json
{
    'sym_variables': [('x1', 'hours worked by Dale'), ('x2', 'hours worked by Hank')],
    'objective_function': '4*x1**2 + 6*x1*x2 + 7*x1',
    'constraints': [
        '4*x1 <= 82',
        '4*x2 <= 82',
        '4*x1 + 4*x2 >= 29',
        '-8*x1 + 6*x2 >= 0',
        '4*x1 + 4*x2 <= 70'
    ]
}
```

### Gurobi Code:

Now, let's implement this optimization problem using Gurobi in Python. We'll use the `gurobipy` library to formulate and solve the model.

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="hours_worked_by_Dale", lb=0)  # Hours worked by Dale
x2 = m.addVar(name="hours_worked_by_Hank", lb=0)   # Hours worked by Hank

# Set the objective function
m.setObjective(4*x1**2 + 6*x1*x2 + 7*x1, GRB.MAXIMIZE)

# Add constraints
m.addConstr(4*x1 <= 82, name="Dale_competence_rating")
m.addConstr(4*x2 <= 82, name="Hank_competence_rating")
m.addConstr(4*x1 + 4*x2 >= 29, name="Min_total_competence_rating")
m.addConstr(-8*x1 + 6*x2 >= 0, name="Specific_linear_constraint")
m.addConstr(4*x1 + 4*x2 <= 70, name="Max_total_competence_rating")

# Optimize the model
m.optimize()

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