## Symbolic Representation

Let's denote:
- \(x_1\) as the number of DVD players produced
- \(x_2\) as the number of projectors produced

The objective is to maximize profit. The profit per DVD player is $250, and per projector is $200. So, the objective function is:

\[ \text{Maximize:} \quad 250x_1 + 200x_2 \]

The constraints based on the given resources and demands are:

1. Silicon chips: \(5x_1 + 3x_2 \leq 250\)
2. Engineering time: \(6x_1 + 5x_2 \leq 200\)
3. Assembly time: \(2.5x_1 + 2x_2 \leq 240\)
4. Minimum DVD players: \(x_1 \geq 30\)
5. Minimum projectors: \(x_2 \geq 30\)
6. Non-negativity: \(x_1, x_2 \geq 0\)

However, since \(x_1\) and \(x_2\) represent quantities of products, they are implicitly non-negative.

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'DVD players'), ('x2', 'projectors')],
    'objective_function': '250*x1 + 200*x2',
    'constraints': [
        '5*x1 + 3*x2 <= 250',
        '6*x1 + 5*x2 <= 200',
        '2.5*x1 + 2*x2 <= 240',
        'x1 >= 30',
        'x2 >= 30'
    ]
}
```

## Gurobi Code in Python

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name='DVD_players', lb=0)  # Number of DVD players
    x2 = model.addVar(name='projectors', lb=0)   # Number of projectors

    # Objective function: Maximize profit
    model.setObjective(250 * x1 + 200 * x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(5 * x1 + 3 * x2 <= 250, name='silicon_chips')
    model.addConstr(6 * x1 + 5 * x2 <= 200, name='engineering_time')
    model.addConstr(2.5 * x1 + 2 * x2 <= 240, name='assembly_time')
    model.addConstr(x1 >= 30, name='min_DVD_players')
    model.addConstr(x2 >= 30, name='min_projectors')

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: DVD players = {x1.varValue}, projectors = {x2.varValue}")
        print(f"Maximum profit: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```