```json
{
  "sym_variables": [
    ("x1", "small PCB's"),
    ("x2", "large PCB's")
  ],
  "objective_function": "Maximize: 20*x1 + 35*x2",
  "constraints": [
    "3*x1 + 5*x2 <= 250 (Silicon constraint)",
    "30*x1 + 40*x2 <= 800 (Design time constraint)",
    "20*x1 + 30*x2 <= 600 (Soldering time constraint)",
    "x1 >= 5 (Minimum small PCBs)",
    "x2 >= 6 (Minimum large PCBs)",
    "x1, x2 >= 0 (Non-negativity constraint)"

  ]
}
```

```python
import gurobipy as gp

# Create a new model
model = gp.Model("PCB_Production")

# Create variables
small_pcbs = model.addVar(lb=0, vtype=gp.GRB.INTEGER, name="small_pcbs")
large_pcbs = model.addVar(lb=0, vtype=gp.GRB.INTEGER, name="large_pcbs")


# Set objective function
model.setObjective(20 * small_pcbs + 35 * large_pcbs, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(3 * small_pcbs + 5 * large_pcbs <= 250, "silicon_constraint")
model.addConstr(30 * small_pcbs + 40 * large_pcbs <= 800, "design_constraint")
model.addConstr(20 * small_pcbs + 30 * large_pcbs <= 600, "soldering_constraint")
model.addConstr(small_pcbs >= 5, "min_small_pcbs")
model.addConstr(large_pcbs >= 6, "min_large_pcbs")


# Optimize model
model.optimize()

# Print results
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal Solution Found:")
    print(f"Number of small PCBs to produce: {small_pcbs.x}")
    print(f"Number of large PCBs to produce: {large_pcbs.x}")
    print(f"Maximum Profit: ${model.objVal}")
elif model.status == gp.GRB.INFEASIBLE:
    print("The model is infeasible.")
else:
    print(f"Optimization terminated with status {model.status}")

```
