## Symbolic Representation

The problem can be converted into a symbolic representation as follows:

Let's denote:
- $x_1$ as the number of bikes
- $x_2$ as the number of cars

The objective function to maximize profit is: $1000x_1 + 3000x_2$

The constraints based on machine availability are:
- Assembly machine: $1x_1 + 3x_2 \leq 10$
- Painting machine: $0.5x_1 + 1x_2 \leq 8$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'bikes'), ('x2', 'cars')],
    'objective_function': '1000*x1 + 3000*x2',
    'constraints': [
        '1*x1 + 3*x2 <= 10',
        '0.5*x1 + 1*x2 <= 8',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

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

# Objective function: maximize profit
model.setObjective(1000*x1 + 3000*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 + 3*x2 <= 10, name="assembly_machine")
model.addConstr(0.5*x1 + x2 <= 8, name="painting_machine")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Bikes to produce: {x1.varValue}")
    print(f"Cars to produce: {x2.varValue}")
    print(f"Max Profit: {model.objVal}")
else:
    print("No optimal solution found.")
```