To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints algebraically.

Let's define:
- \(x_1\) as the number of marble countertops produced,
- \(x_2\) as the number of granite countertops produced.

The objective is to maximize profit, which can be represented by the objective function:
\[500x_1 + 750x_2\]

Given the constraints:
1. Cutting time: \(x_1 + 1.5x_2 \leq 300\)
2. Polishing time: \(2x_1 + 3x_2 \leq 500\)
3. Non-negativity: \(x_1, x_2 \geq 0\) (since we cannot produce a negative number of countertops)

The symbolic representation of the problem is:
```json
{
  'sym_variables': [('x1', 'marble countertops'), ('x2', 'granite countertops')],
  'objective_function': '500*x1 + 750*x2',
  'constraints': ['x1 + 1.5*x2 <= 300', '2*x1 + 3*x2 <= 500', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we will use the following code:

```python
from gurobipy import *

# Create a new model
m = Model("Countertops")

# Define variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="marble_countertops")
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="granite_countertops")

# Set the objective function
m.setObjective(500*x1 + 750*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + 1.5*x2 <= 300, "cutting_time")
m.addConstr(2*x1 + 3*x2 <= 500, "polishing_time")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Marble Countertops: {x1.x}")
    print(f"Granite Countertops: {x2.x}")
    print(f"Maximum Profit: ${500*x1.x + 750*x2.x:.2f}")
else:
    print("No optimal solution found")
```