## Problem Description and Formulation

The engineering company produces small and large PCB's with different requirements for silicon, design time, and soldering time. The goal is to maximize profit given the constraints on resources and minimum production requirements.

### Variables
- \(S\): Number of small PCB's to produce
- \(L\): Number of large PCB's to produce

### Objective Function
Maximize profit \(P = 20S + 35L\)

### Constraints
1. Silicon: \(3S + 5L \leq 250\)
2. Design Time: \(30S + 40L \leq 800\)
3. Soldering Time: \(20S + 30L \leq 600\)
4. Minimum Small PCB's: \(S \geq 5\)
5. Minimum Large PCB's: \(L \geq 6\)
6. Non-negativity and Integer: \(S, L \geq 0\) and \(S, L\) are integers

## Gurobi Code

```python
import gurobipy as gp

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

# Variables
S = m.addVar(lb=5, name="Small_PCBs", vtype=gp.GRB.INTEGER)  # Minimum 5 small PCB's
L = m.addVar(lb=6, name="Large_PCBs", vtype=gp.GRB.INTEGER)  # Minimum 6 large PCB's

# Objective function: Maximize profit
m.setObjective(20*S + 35*L, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(3*S + 5*L <= 250, name="Silicon_Constraint")
m.addConstr(30*S + 40*L <= 800, name="Design_Time_Constraint")
m.addConstr(20*S + 30*L <= 600, name="Soldering_Time_Constraint")

# Solve the model
m.solve()

# Output solution
if m.status == gp.GRB.OPTIMAL:
    print(f"Optimal Solution: Produce {S.varValue} small PCB's and {L.varValue} large PCB's")
else:
    print("The model is infeasible")
```