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

Let's denote:
- $x_1$ as the number of moving seat tickets sold
- $x_2$ as the number of regular seat tickets sold

The objective is to maximize profit. The profit made on each moving seat ticket is $15, and on each regular seat ticket is $10. Therefore, the objective function can be represented as: $15x_1 + 10x_2$.

## Step 2: Identify the constraints

1. The theatre can seat at most 100 people: $x_1 + x_2 \leq 100$
2. The theatre reserves at least 15 seats to be moving seats: $x_1 \geq 15$
3. At least 3 times as many people prefer sitting in regular seats than in moving seats: $x_2 \geq 3x_1$

## 3: Symbolic representation of the problem

```json
{
'sym_variables': [('x1', 'moving seat tickets'), ('x2', 'regular seat tickets')],
'objective_function': '15*x1 + 10*x2',
'constraints': [
    'x1 + x2 <= 100',
    'x1 >= 15',
    'x2 >= 3*x1'
]
}
```

## Step 4: Convert the problem into Gurobi code

To solve this linear programming problem using Gurobi, we will use the Gurobi Python API.

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=0, name="moving_seats")  # Number of moving seat tickets
    x2 = model.addVar(lb=0, name="regular_seats")  # Number of regular seat tickets

    # Objective function: maximize 15*x1 + 10*x2
    model.setObjective(15*x1 + 10*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 100, name="total_seats")
    model.addConstr(x1 >= 15, name="min_moving_seats")
    model.addConstr(x2 >= 3*x1, name="regular_vs_moving")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Moving seat tickets: {x1.varValue}")
        print(f"Regular seat tickets: {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_movie_theatre_problem()
```