## Symbolic Representation

Let's denote:
- $x_1$ as the number of small PCB's
- $x_2$ as the number of large PCB's

The objective is to maximize profit, which is $20x_1 + 35x_2$.

The constraints are:
- $3x_1 + 5x_2 \leq 250$ (silicon units)
- $30x_1 + 40x_2 \leq 800$ (design time in minutes)
- $20x_1 + 30x_2 \leq 600$ (soldering time in minutes)
- $x_1 \geq 5$ (minimum small PCB's)
- $x_2 \geq 6$ (minimum large PCB's)
- $x_1, x_2 \geq 0$ and are integers (non-negativity and integrality)

However, since Gurobi can handle continuous variables and we will round if necessary, we focus on:
- $x_1, x_2 \geq 0$

## Optimization Problem in Symbolic Notation

```json
{
    'sym_variables': [('x1', 'small PCB\'s'), ('x2', 'large PCB\'s')],
    'objective_function': '20*x1 + 35*x2',
    'constraints': [
        '3*x1 + 5*x2 <= 250',
        '30*x1 + 40*x2 <= 800',
        '20*x1 + 30*x2 <= 600',
        'x1 >= 5',
        'x2 >= 6'
    ]
}
```

## Gurobi Code

```python
import gurobi

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

    # Define variables
    x1 = model.addVar(name='x1', lb=0, vtype=gurobi.GRB.INTEGER)  # small PCB's
    x2 = model.addVar(name='x2', lb=0, vtype=gurobi.GRB.INTEGER)  # large PCB's

    # Objective function: maximize 20*x1 + 35*x2
    model.setObjective(20*x1 + 35*x2, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(3*x1 + 5*x2 <= 250)  # silicon units
    model.addConstr(30*x1 + 40*x2 <= 800)  # design time
    model.addConstr(20*x1 + 30*x2 <= 600)  # soldering time
    model.addConstr(x1 >= 5)  # minimum small PCB's
    model.addConstr(x2 >= 6)  # minimum large PCB's

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: x1 = {x1.varValue}, x2 = {x2.varValue}")
        print(f"Maximum profit: ${20*x1.varValue + 35*x2.varValue}")
    else:
        print("No optimal solution found.")

solve_pcb_problem()
```