To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables for the quantities of cars and trucks to be produced, formulating the objective function that represents the total profit, and listing the constraints based on the available resources (assembly line time and mechanic time).

Let's define:
- \(x_1\) as the number of cars to be made,
- \(x_2\) as the number of trucks to be made.

The objective function aims to maximize profit. Given that each car generates a profit of $5000 and each truck generates a profit of $8000, the objective function can be written as:
\[ \text{Maximize:} \quad 5000x_1 + 8000x_2 \]

The constraints are based on the available assembly line time and mechanic time. Each car requires 2 hours of assembly line time and 1 hour of mechanic time, while each truck requires 2.5 hours of assembly line time and 1.5 hours of mechanic time. With 800 hours of assembly line time and 600 hours of mechanic time available, the constraints can be formulated as:
\[ 2x_1 + 2.5x_2 \leq 800 \] (assembly line time constraint)
\[ x_1 + 1.5x_2 \leq 600 \] (mechanic time constraint)

Additionally, \(x_1\) and \(x_2\) must be non-negative since they represent quantities of cars and trucks.

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of cars'), ('x2', 'number of trucks')],
    'objective_function': '5000*x1 + 8000*x2',
    'constraints': ['2*x1 + 2.5*x2 <= 800', 'x1 + 1.5*x2 <= 600', 'x1 >= 0', 'x2 >= 0']
}
```

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

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="cars")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="trucks")

# Set the objective function
m.setObjective(5000*x1 + 8000*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(2*x1 + 2.5*x2 <= 800, "assembly_line_time")
m.addConstr(x1 + 1.5*x2 <= 600, "mechanic_time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of cars: {x1.x}")
    print(f"Number of trucks: {x2.x}")
    print(f"Total profit: ${5000*x1.x + 8000*x2.x:.2f}")
else:
    print("No optimal solution found")
```