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 using these variables.

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, which can be represented by the objective function: $15x_1 + 10x_2$.

Given constraints are:
1. The total number of seats is limited to 100: $x_1 + x_2 \leq 100$.
2. At least 15 seats must be reserved for moving seats: $x_1 \geq 15$.
3. At least 3 times as many people prefer sitting in regular seats than in moving seats: $x_2 \geq 3x_1$.

The symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of moving seat tickets sold'), ('x2', 'number of regular seat tickets sold')],
    'objective_function': '15*x1 + 10*x2',
    'constraints': ['x1 + x2 <= 100', 'x1 >= 15', 'x2 >= 3*x1']
}
```

To solve this linear programming problem using Gurobi in Python, we can use the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="moving_seat_tickets")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="regular_seat_tickets")

# Set the objective function
m.setObjective(15*x1 + 10*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 100, "total_seats")
m.addConstr(x1 >= 15, "minimum_moving_seats")
m.addConstr(x2 >= 3*x1, "regular_vs_moving_seats")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Moving seat tickets: {x1.x}")
    print(f"Regular seat tickets: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```