To solve the given optimization problem, let's first convert the natural language description into a symbolic representation.

The variables can be represented as follows:
- Let $x_1$ represent the number of adult tickets sold.
- Let $x_2$ represent the number of children's tickets sold.

The objective function is to maximize profit. Given that a profit of $3 is made on each adult ticket and a profit of $1 is made on each children's ticket, the objective function can be represented algebraically as:
\[ 3x_1 + x_2 \]

The constraints are:
1. The bus can carry at most 80 people: \( x_1 + x_2 \leq 80 \)
2. At least 15 tickets are reserved for children: \( x_2 \geq 15 \)
3. At least 3 times as many tickets sold are adult tickets than children's tickets: \( x_1 \geq 3x_2 \)

Additionally, since the number of tickets cannot be negative, we also have:
- \( x_1 \geq 0 \)
- \( x_2 \geq 0 \)

Therefore, in symbolic notation with natural language objects, our problem can be represented as:
```json
{
  'sym_variables': [('x1', 'number of adult tickets sold'), ('x2', 'number of children\'s tickets sold')],
  'objective_function': '3*x1 + x2',
  'constraints': ['x1 + x2 <= 80', 'x2 >= 15', 'x1 >= 3*x2', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:
```python
from gurobipy import *

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

# Define the variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="adult_tickets")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="children_tickets")

# Set the objective function
m.setObjective(3*x1 + x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 + x2 <= 80, "total_capacity")
m.addConstr(x2 >= 15, "children_reserved")
m.addConstr(x1 >= 3*x2, "adult_to_children_ratio")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Adult tickets: {x1.x}")
    print(f"Children tickets: {x2.x}")
    print(f"Maximum profit: {m.objVal}")
else:
    print("No optimal solution found")
```