To solve this problem, we first need to define the symbolic representation of the variables and the optimization problem.

Let's denote:
- $x_1$ as the number of packages of drills produced.
- $x_2$ as the number of packages of saws produced.

The objective function, which represents the total profit, can be written as:
\[ 35x_1 + 100x_2 \]

This is because each package of drills contributes $35 to the profit and each package of saws contributes $100.

The constraints are based on the time availability of the machines and the production times for each type of tool. Specifically:
- The milling machine constraint: $20x_1 + 30x_2 \leq 800$
- The CNG machine constraint: $70x_1 + 90x_2 \leq 800$
- Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$ (since the number of packages produced cannot be negative)

Thus, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of packages of drills'), ('x2', 'number of packages of saws')],
    'objective_function': '35*x1 + 100*x2',
    'constraints': ['20*x1 + 30*x2 <= 800', '70*x1 + 90*x2 <= 800', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this linear programming problem, we can use the Gurobi solver in Python. Here's how you could implement it:

```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(name="drills", vtype=GRB.CONTINUOUS, lb=0)
x2 = m.addVar(name="saws", vtype=GRB.CONTINUOUS, lb=0)

# Set the objective function
m.setObjective(35*x1 + 100*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x1 + 30*x2 <= 800, name="milling_machine")
m.addConstr(70*x1 + 90*x2 <= 800, name="CNG_machine")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Produced drills: {x1.x}")
    print(f"Produced saws: {x2.x}")
    print(f"Maximum profit: ${m.objVal:.2f}")
else:
    print("No optimal solution found")
```