## Symbolic Representation

To solve the given problem, we first need to convert the natural language description into a symbolic representation.

Let's define the symbolic variables as follows:
- $x_1$ represents the number of televisions sold.
- $x_2$ represents the number of speakers sold.

The objective is to maximize profit. Given that the profit per television sold is $400 and the profit per speaker sold is $250, the objective function can be represented as:
\[ \text{Maximize:} \quad 400x_1 + 250x_2 \]

The constraints based on the problem description are:
1. The store can spend at most $25000, with a television costing $400 and a speaker costing $200:
\[ 400x_1 + 200x_2 \leq 25000 \]
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 a half of the number of televisions sold:
\[ x_2 \leq 0.5x_1 \]
4. Non-negativity constraints (number of items cannot be negative):
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

However, since $x_1$ and $x_2$ represent the number of items, they should be integers.

## Symbolic Representation in JSON Format

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

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(lb=0, ub=75, vtype=gurobi.GRB.INTEGER, name="televisions")
    x2 = model.addVar(lb=0, vtype=gurobi.GRB.INTEGER, name="speakers")

    # Objective function: Maximize 400*x1 + 250*x2
    model.setObjective(400*x1 + 250*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(400*x1 + 200*x2 <= 25000, name="budget_constraint")
    model.addConstr(x1 >= 20, name="min_televisions_constraint")
    model.addConstr(x2 <= 0.5*x1, name="speakers_vs_televisions_constraint")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: Televisions = {x1.varValue}, Speakers = {x2.varValue}")
        print(f"Max Profit: {model.objVal}")
    else:
        print("No optimal solution found")

solve_optimization_problem()
```