## Step 1: Define the symbolic representation of the problem

Let's denote the number of display shelves as $x_1$ and the number of plant stands as $x_2$. The objective is to maximize the profit, which is $55x_1 + 45x_2$. The constraints are:

- Carving time: $25x_1 + 20x_2 \leq 350$
- Polishing time: $20x_1 + 10x_2 \leq 600$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Step 2: Convert the problem into a Gurobi-compatible format

The symbolic representation of the variables and the problem is as follows:
```json
{
    'sym_variables': [('x1', 'display shelf'), ('x2', 'plant stand')],
    'objective_function': '55*x1 + 45*x2',
    'constraints': [
        '25*x1 + 20*x2 <= 350',
        '20*x1 + 10*x2 <= 600',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Step 3: Write the Gurobi code in Python

Now, let's write the Gurobi code to solve this problem:
```python
import gurobi

def solve_optimization_problem():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x1 = model.addVar(name="display_shelf", lb=0, vtype=gurobi.GRB.CONTINUOUS)
    x2 = model.addVar(name="plant_stand", lb=0, vtype=gurobi.GRB.CONTINUOUS)

    # Set the objective function
    model.setObjective(55 * x1 + 45 * x2, gurobi.GRB.MAXIMIZE)

    # Add the constraints
    model.addConstr(25 * x1 + 20 * x2 <= 350, name="carving_time")
    model.addConstr(20 * x1 + 10 * x2 <= 600, name="polishing_time")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Display shelves: {x1.varValue}")
        print(f"Plant stands: {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```