To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation. Let's denote the amount of maple syrup produced as \(x_1\) and the amount of maple candy produced as \(x_2\).

The symbolic representation of the variables is:
- \(x_1\): Amount of maple syrup (in kg)
- \(x_2\): Amount of maple candy (in kg)

The objective function, which aims to maximize profit, can be represented algebraically using these symbolic variables. Given that the profit per kg of maple syrup is $20 and the profit per kg of maple candy is $15, the objective function is:
\[ \text{Maximize: } 20x_1 + 15x_2 \]

The constraints based on the problem description are:
1. The farm can make at most 10 kg of maple syrup: \( x_1 \leq 10 \)
2. The farm can make at most 12 kg of maple candy: \( x_2 \leq 12 \)
3. The farm must supply at least 3 kg of maple syrup per day: \( x_1 \geq 3 \)
4. The farm must supply at least 5 kg of maple candy per day: \( x_2 \geq 5 \)
5. Both products require time in a maple boiling station, with each kg requiring 2 hours, and the boiling station is available for at most 20 hours per day: \( 2x_1 + 2x_2 \leq 20 \)

Thus, the symbolic representation of the problem can be summarized as:
```json
{
    'sym_variables': [('x1', 'Amount of maple syrup'), ('x2', 'Amount of maple candy')],
    'objective_function': 'Maximize: 20*x1 + 15*x2',
    'constraints': ['x1 <= 10', 'x2 <= 12', 'x1 >= 3', 'x2 >= 5', '2*x1 + 2*x2 <= 20']
}
```

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("Maple_Farm_Profit")

# Add variables
x1 = m.addVar(name="maple_syrup", lb=3, ub=10)  # Amount of maple syrup (kg)
x2 = m.addVar(name="maple_candy", lb=5, ub=12)  # Amount of maple candy (kg)

# Set the objective function
m.setObjective(20*x1 + 15*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 10, name="max_syrup")
m.addConstr(x2 <= 12, name="max_candy")
m.addConstr(2*x1 + 2*x2 <= 20, name="boiling_station_time")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution found:")
    print(f"Maple Syrup: {x1.x} kg")
    print(f"Maple Candy: {x2.x} kg")
    print(f"Maximum Profit: ${m.objVal}")
else:
    print("No optimal solution found.")
```