## Symbolic Representation

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

Let's denote:
- $x_1$ as the number of marble countertops
- $x_2$ as the number of granite countertops

The objective function to maximize profit is:
\[ \text{Maximize:} \quad 500x_1 + 750x_2 \]

The constraints based on the available hours for cutting and polishing are:
\[ \text{Subject to:} \quad 
\begin{align*}
1x_1 + 1.5x_2 &\leq 300 \quad \text{(Cutting hours constraint)} \\
2x_1 + 3x_2 &\leq 500 \quad \text{(Polishing hours constraint)} \\
x_1, x_2 &\geq 0 \quad \text{(Non-negativity constraint)}
\end{align*}
\]

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'marble countertops'), ('x2', 'granite countertops')],
    'objective_function': '500*x1 + 750*x2',
    'constraints': [
        '1*x1 + 1.5*x2 <= 300',
        '2*x1 + 3*x2 <= 500',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

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

# Objective function
model.setObjective(500*x1 + 750*x2, gp.GRB.MAXIMIZE)

# Constraints
model.addConstr(x1 + 1.5*x2 <= 300, name="cutting_hours_constraint")
model.addConstr(2*x1 + 3*x2 <= 500, name="polishing_hours_constraint")

# Solve the model
model.optimize()

# Print the results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal number of marble countertops: {x1.varValue}")
    print(f"Optimal number of granite countertops: {x2.varValue}")
    print(f"Maximal profit: {model.objVal}")
else:
    print("The model is infeasible or unbounded.")
```