## Step 1: Define the symbolic representation of the problem
Let's denote:
- $x_1$ as the number of all-inclusive tickets sold
- $x_2$ as the number of regular tickets sold

The objective is to maximize profit, given that the profit per all-inclusive ticket is $50 and the profit per regular ticket is $20. Therefore, the objective function can be represented as $50x_1 + 20x_2$.

## Step 2: Identify the constraints
From the problem description, we have the following constraints:
1. The company sells 500 tickets in a day due to capacity constraint: $x_1 + x_2 = 500$
2. They reserve at least 100 of them to be all-inclusive tickets: $x_1 \geq 100$
3. At least 3 times as many people prefer regular tickets than all-inclusive tickets: $x_2 \geq 3x_1$
4. Non-negativity constraints: $x_1 \geq 0, x_2 \geq 0$

However, since $x_1$ and $x_2$ represent the number of tickets, they must be integers, but for the purpose of linear programming, we'll consider them as continuous variables first.

## 3: Symbolic representation in JSON format
```json
{
'sym_variables': [('x1', 'all-inclusive tickets'), ('x2', 'regular tickets')],
'objective_function': '50*x1 + 20*x2',
'constraints': [
'x1 + x2 <= 500',
'x1 >= 100',
'x2 >= 3*x1',
'x1 >= 0',
'x2 >= 0'
]
}
```

## 4: Convert the problem into Gurobi code
To solve this linear programming problem using Gurobi in Python, we will use the following code:

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=0, name="all_inclusive_tickets")
    x2 = model.addVar(lb=0, name="regular_tickets")

    # Objective function: maximize 50*x1 + 20*x2
    model.setObjective(50*x1 + 20*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(x1 + x2 <= 500, name="capacity_constraint")
    model.addConstr(x1 >= 100, name="all_inclusive_min")
    model.addConstr(x2 >= 3*x1, name="regular_vs_all_inclusive")

    # Solve the model
    model.optimize()

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

solve_problem()
```

This code defines the variables, sets up the objective function and constraints, solves the linear programming problem, and then prints out the optimal solution if one is found.