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

Let's define the symbolic variables:
- $x_1$ = number of regular passes
- $x_2$ = number of premium passes

The objective function is to maximize profit: $40x_1 + 90x_2$

## Step 2: List the constraints

The constraints based on the problem description are:
1. The movie theatre can sell at most 500 passes: $x_1 + x_2 \leq 500$
2. The theatre reserves at least 100 passes to be premium: $x_2 \geq 100$
3. At least 3 times as many people prefer to buy regular passes than premium passes: $x_1 \geq 3x_2$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

## 3: Convert the problem into a Gurobi-compatible format

## Step 4: Write down the symbolic representation in the required format

```json
{
'sym_variables': [('x1', 'regular passes'), ('x2', 'premium passes')],
'objective_function': '40*x1 + 90*x2',
'constraints': [
    'x1 + x2 <= 500',
    'x2 >= 100',
    'x1 >= 3*x2',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## 5: Implement the problem in Gurobi

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(name="regular_passes", lb=0, ub=gurobi.GRB.INFINITY)
    x2 = model.addVar(name="premium_passes", lb=0, ub=gurobi.GRB.INFINITY)

    # Objective function: maximize 40*x1 + 90*x2
    model.setObjective(40*x1 + 90*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 500, name="total_passes")
    model.addConstr(x2 >= 100, name="premium_passes_min")
    model.addConstr(x1 >= 3*x2, name="regular_to_premium_ratio")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: regular passes = {x1.varValue}, premium passes = {x2.varValue}")
    else:
        print("No optimal solution found")

solve_movie_theatre_problem()
```