## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation.

Let's define the variables:
- $x_1$ = number of cars
- $x_2$ = number of trucks

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

The constraints based on the given resources are:
- Assembly line time: $2x_1 + 2.5x_2 \leq 800$
- Mechanic time: $x_1 + 1.5x_2 \leq 600$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'cars'), ('x2', 'trucks')],
    'objective_function': '5000*x1 + 8000*x2',
    'constraints': [
        '2*x1 + 2.5*x2 <= 800',
        'x1 + 1.5*x2 <= 600',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("AutoPlantProduction")

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

# Objective function: Maximize profit
model.setObjective(5000*x1 + 8000*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(2*x1 + 2.5*x2 <= 800, name="assembly_line_time")
model.addConstr(x1 + 1.5*x2 <= 600, name="mechanic_time")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal number of cars: {x1.varValue}")
    print(f"Optimal number of trucks: {x2.varValue}")
    print(f"Maximal profit: {model.objVal}")
else:
    print("The model is infeasible.")
```