## Step 1: Define the symbolic representation of the problem

Let's denote:
- $x_1$ as the number of regular laptops
- $x_2$ as the number of touchscreen laptops

The objective is to maximize profit, where the profit per regular laptop is $200 and per touchscreen laptop is $300. Therefore, the objective function is $200x_1 + 300x_2$.

## Step 2: Define the constraints

The company has available 3000 minutes for manual labor and 2000 minutes for calibration.
- Each regular laptop takes 20 minutes of manual labor and 10 minutes of calibration.
- Each touchscreen laptop takes 25 minutes of manual labor and 20 minutes of calibration.

This translates into the following constraints:
1. Manual labor constraint: $20x_1 + 25x_2 \leq 3000$
2. Calibration constraint: $10x_1 + 20x_2 \leq 2000$
Also, $x_1 \geq 0$ and $x_2 \geq 0$ because the number of laptops cannot be negative.

## 3: Symbolic representation in JSON format

```json
{
'sym_variables': [('x1', 'regular laptops'), ('x2', 'touchscreen laptops')],
'objective_function': '200*x1 + 300*x2',
'constraints': [
    '20*x1 + 25*x2 <= 3000',
    '10*x1 + 20*x2 <= 2000',
    'x1 >= 0',
    'x2 >= 0'
]
}
```

## Step 4: Gurobi code in Python

```python
import gurobi

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

    # Define the variables
    x1 = model.addVar(lb=0, name="regular_laptops")
    x2 = model.addVar(lb=0, name="touchscreen_laptops")

    # Define the objective function
    model.setObjective(200*x1 + 300*x2, gurobi.GRB.MAXIMIZE)

    # Define the constraints
    model.addConstr(20*x1 + 25*x2 <= 3000, name="manual_labor_constraint")
    model.addConstr(10*x1 + 20*x2 <= 2000, name="calibration_constraint")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Number of regular laptops: {x1.varValue}")
        print(f"Number of touchscreen laptops: {x2.varValue}")
        print(f"Max profit: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```