## Step 1: Define the symbolic representation of the problem
Let's denote the number of cars to be produced as $x_1$ and the number of bikes to be produced as $x_2$. The objective is to maximize profit, where each car nets $5000 and each bike nets $1000.

## Step 2: Formulate the objective function
The objective function to maximize profit can be written as $5000x_1 + 1000x_2$.

## 3: Identify the constraints
1. Steel constraint: Both vehicles require 30 kg of steel, and the company receives 1000 kg of steel each week. This can be represented as $30x_1 + 30x_2 \leq 1000$.
2. Engineering time constraint: A car requires 3 hours of engineering time, and a bike requires 1 hour. With 400 hours available, this can be represented as $3x_1 + x_2 \leq 400$.
3. Non-negativity constraints: $x_1 \geq 0$ and $x_2 \geq 0$, as the number of vehicles cannot be negative.

## 4: Convert the problem into a symbolic representation
The symbolic representation is:
```json
{
'sym_variables': [('x1', 'cars'), ('x2', 'bikes')],
'objective_function': '5000*x1 + 1000*x2',
'constraints': [
    '30*x1 + 30*x2 <= 1000',
    '3*x1 + x2 <= 400',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 5: Translate the symbolic representation into Gurobi code
Now, let's write the Gurobi code in Python to solve this linear programming problem.

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="cars", lb=0)  # Number of cars
x2 = model.addVar(name="bikes", lb=0)  # Number of bikes

# Define the objective function
model.setObjective(5000*x1 + 1000*x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(30*x1 + 30*x2 <= 1000, name="steel_constraint")
model.addConstr(3*x1 + x2 <= 400, name="engineering_time_constraint")

# Solve the model
model.optimize()

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