To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints.

Let's define:
- $x_1$ as the number of televisions sold,
- $x_2$ as the number of speakers sold.

The profit per television is $400, and the profit per speaker is $250. Therefore, the total profit can be represented by the objective function:
\[ \text{Maximize: } 400x_1 + 250x_2 \]

The constraints are as follows:
1. The store can spend at most $25,000 on televisions and speakers. Given that a television costs $400 and a speaker costs $200, we have:
\[ 400x_1 + 200x_2 \leq 25000 \]
2. The store sells at least 20 televisions but at most 75 televisions:
\[ 20 \leq x_1 \leq 75 \]
3. The number of speakers sold is at most half the number of televisions sold:
\[ x_2 \leq \frac{1}{2}x_1 \]

All variables are non-negative since they represent quantities of items.

Thus, the symbolic representation of the problem is:

```json
{
  'sym_variables': [('x1', 'number of televisions'), ('x2', 'number of speakers')],
  'objective_function': '400*x1 + 250*x2',
  'constraints': [
    '400*x1 + 200*x2 <= 25000',
    '20 <= x1 <= 75',
    'x2 <= 0.5*x1',
    'x1 >= 0',
    'x2 >= 0'
  ]
}
```

Now, let's implement this problem in Gurobi using Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name='x1', lb=20, ub=75, vtype=GRB.INTEGER)
x2 = m.addVar(name='x2', lb=0, vtype=GRB.INTEGER)

# Set the objective function
m.setObjective(400*x1 + 250*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(400*x1 + 200*x2 <= 25000, name='budget')
m.addConstr(x2 <= 0.5*x1, name='speaker_limit')

# Optimize the model
m.optimize()

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