Here's the formulation of the linear program and the Gurobi code to solve it:

**Decision Variables:**

* `d`: Number of doors to produce
* `b`: Number of bumpers to produce

**Objective Function:**

Maximize profit: `200d + 150b`

**Constraints:**

* **Machine Time:** `20d + 10b <= 3000` (Total machine time used cannot exceed available time)
* **Door Production Limit:** `d <= 100` (Maximum number of doors)
* **Bumper Production Limit:** `b <= 200` (Maximum number of bumpers)
* **Non-negativity:** `d >= 0`, `b >= 0` (Cannot produce negative quantities)


```python
import gurobipy as gp

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

# Create decision variables
d = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="doors") # Doors are assumed to be continuously divisible
b = m.addVar(lb=0, vtype=gp.GRB.CONTINUOUS, name="bumpers")

# Set objective function
m.setObjective(200*d + 150*b, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*d + 10*b <= 3000, "machine_time")
m.addConstr(d <= 100, "door_limit")
m.addConstr(b <= 200, "bumper_limit")

# Optimize model
m.optimize()

# Print results
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of Doors: {d.x}")
    print(f"Number of Bumpers: {b.x}")
    print(f"Maximum Profit: ${m.objVal}")
elif m.status == gp.GRB.INFEASIBLE:
    print("Model is infeasible.")
else:
    print(f"Optimization terminated with status {m.status}")

```
