To solve the optimization problem described, 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 denote:
- \(x_1\) as the number of laptops made,
- \(x_2\) as the number of tablets made.

The profit per laptop is $200, and the profit per tablet is $160. Thus, the objective function to maximize profit can be written as:
\[ \text{Maximize:} \quad 200x_1 + 160x_2 \]

The constraints are based on the manufacturing time and silicon availability:
- Each laptop takes 20 minutes of manufacturing time, and each tablet takes 15 minutes. The total available manufacturing time is 1200 minutes. This gives us the constraint:
\[ 20x_1 + 15x_2 \leq 1200 \]
- The company requires at least 30 laptops to be made:
\[ x_1 \geq 30 \]
- Each laptop requires 3 units of silicon, and each tablet requires 2 units. The total available silicon is 150 units:
\[ 3x_1 + 2x_2 \leq 150 \]
- Non-negativity constraints (since the number of laptops and tablets cannot be negative):
\[ x_1 \geq 0, \quad x_2 \geq 0 \]

Thus, the symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of laptops'), ('x2', 'number of tablets')],
    'objective_function': '200*x1 + 160*x2',
    'constraints': ['20*x1 + 15*x2 <= 1200', 'x1 >= 30', '3*x1 + 2*x2 <= 150', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we use the following code:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(name="laptops", vtype=GRB.INTEGER)
x2 = m.addVar(name="tablets", vtype=GRB.INTEGER)

# Set objective function
m.setObjective(200*x1 + 160*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(20*x1 + 15*x2 <= 1200, name="manufacturing_time")
m.addConstr(x1 >= 30, name="minimum_laptops")
m.addConstr(3*x1 + 2*x2 <= 150, name="silicon_availability")
m.addConstr(x1 >= 0, name="non_negative_laptops")
m.addConstr(x2 >= 0, name="non_negative_tablets")

# Optimize model
m.optimize()

# Print solution
if m.status == GRB.OPTIMAL:
    print(f"Optimal solution: {x1.varName} = {x1.x}, {x2.varName} = {x2.x}")
    print(f"Maximum Profit: ${200*x1.x + 160*x2.x}")
else:
    print("No optimal solution found")
```