To solve this optimization problem, we first need to define the decision variables and the constraints based on the given information. Let's denote:

- \(x_1\) as the number of DVD players produced per week.
- \(x_2\) as the number of projectors produced per week.

The objective function is to maximize profit. The profit per DVD player is $250, and the profit per projector is $200. Therefore, the total profit \(P\) can be represented as:

\[ P = 250x_1 + 200x_2 \]

Now, let's define the constraints based on the limited resources:

1. **Silicon Chips Constraint**: Each DVD player requires 5 silicon chips, and each projector requires 3 silicon chips. The company can buy up to 250 silicon chips per week. This constraint can be represented as:

\[ 5x_1 + 3x_2 \leq 250 \]

2. **Engineering Time Constraint**: Each DVD player requires 6 hours of engineering time, and each projector requires 5 hours of engineering time. There are 200 hours of engineering time available per week. This constraint can be represented as:

\[ 6x_1 + 5x_2 \leq 200 \]

3. **Assembly Time Constraint**: Each DVD player requires 2.5 hours of assembly time, and each projector requires 2 hours of assembly time. There are 240 hours of assembly time available per week. This constraint can be represented as:

\[ 2.5x_1 + 2x_2 \leq 240 \]

4. **Minimum Production Constraints**: The company wants to produce at least 30 units of DVD players and at least 30 units of projectors each week. These constraints can be represented as:

\[ x_1 \geq 30 \]
\[ x_2 \geq 30 \]

5. **Non-Negativity Constraints**: Since the number of units produced cannot be negative, we have:

\[ x_1 \geq 0 \]
\[ x_2 \geq 0 \]

However, given that we already have minimum production levels specified, the non-negativity constraints are implicitly satisfied by the minimum production constraints.

Now, let's translate these constraints and the objective function into Gurobi code in Python:

```python
from gurobipy import *

# Create a model
m = Model("Electronics_Factory")

# Decision variables
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="DVD_players", lb=30)
x2 = m.addVar(vtype=GRB.CONTINUOUS, name="projectors", lb=30)

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

# Constraints
m.addConstr(5*x1 + 3*x2 <= 250, "silicon_chips")
m.addConstr(6*x1 + 5*x2 <= 200, "engineering_time")
m.addConstr(2.5*x1 + 2*x2 <= 240, "assembly_time")

# Optimize the model
m.optimize()

# Print results
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: Produce {x1.x} DVD players and {x2.x} projectors")
    print(f"Maximum profit: ${m.objVal}")
else:
    print("No optimal solution found")
```