## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The goal is to maximize the profit of a circuit board company by determining the optimal number of small and large circuit boards to produce, given the constraints on the availability of drilling and printing machines.

Let's define the decision variables:

* `x`: number of small circuit boards to produce
* `y`: number of large circuit boards to produce

The objective function is to maximize the total profit:

* Profit per small circuit board: $5
* Profit per large circuit board: $7
* Total profit: `5x + 7y`

The constraints are:

* Drilling machine availability: `10x + 15y <= 600` (minutes)
* Printing machine availability: `15x + 18y <= 600` (minutes)
* Non-negativity constraints: `x >= 0`, `y >= 0` (number of circuit boards cannot be negative)

## Gurobi Code

```python
import gurobi

# Create a new Gurobi model
model = gurobi.Model()

# Define the decision variables
x = model.addVar(lb=0, name="small_circuit_boards")
y = model.addVar(lb=0, name="large_circuit_boards")

# Define the objective function
model.setObjective(5 * x + 7 * y, gurobi.GRB.MAXIMIZE)

# Define the constraints
drilling_constraint = model.addConstr(10 * x + 15 * y <= 600, name="drilling_machine")
printing_constraint = model.addConstr(15 * x + 18 * y <= 600, name="printing_machine")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Number of small circuit boards: {x.varValue}")
    print(f"Number of large circuit boards: {y.varValue}")
    print(f"Maximum profit: ${model.objVal:.2f}")
else:
    print("No optimal solution found.")
```

This code defines the decision variables, objective function, and constraints, and then solves the linear programming problem using Gurobi. The solution is printed to the console, including the optimal number of small and large circuit boards to produce and the maximum profit.