To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote:

- \(x_1\) as the number of hockey sticks sold,
- \(x_2\) as the number of pucks sold.

The objective function is to maximize profit. The profit from selling one hockey stick is $50, and from selling one puck is $5. Therefore, the objective function can be represented algebraically as:

\[ \text{Maximize:} \quad 50x_1 + 5x_2 \]

The constraints given are:
1. The total cost of hockey sticks and pucks cannot exceed $20,000.
   - Cost of one hockey stick = $75
   - Cost of one puck = $2
   - Therefore, \(75x_1 + 2x_2 \leq 20000\).

2. At least 50 but at most 110 hockey sticks are sold each month:
   - \(50 \leq x_1 \leq 110\).

3. The number of pucks sold is at most three times the number of hockey sticks sold:
   - \(x_2 \leq 3x_1\).

4. Non-negativity constraints (since we cannot sell a negative number of items):
   - \(x_1 \geq 0, x_2 \geq 0\).

Thus, the symbolic representation of the problem is:

```json
{
    'sym_variables': [('x1', 'number of hockey sticks sold'), ('x2', 'number of pucks sold')],
    'objective_function': '50*x1 + 5*x2',
    'constraints': [
        '75*x1 + 2*x2 <= 20000',
        '50 <= x1 <= 110',
        'x2 <= 3*x1',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

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

```python
from gurobipy import *

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

# Add variables
x1 = m.addVar(vtype=GRB.INTEGER, name="hockey_sticks")
x2 = m.addVar(vtype=GRB.INTEGER, name="pucks")

# Set the objective function
m.setObjective(50*x1 + 5*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(75*x1 + 2*x2 <= 20000, "budget")
m.addConstr(x1 >= 50, "min_hockey_sticks")
m.addConstr(x1 <= 110, "max_hockey_sticks")
m.addConstr(x2 <= 3*x1, "pucks_vs_sticks")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Hockey sticks to sell: {x1.x}")
    print(f"Pucks to sell: {x2.x}")
    print(f"Max Profit: {m.objVal}")
else:
    print("No optimal solution found")
```