To solve this optimization problem, we need to define variables and constraints that capture the essence of the problem. Let's denote:

- $x$ as the number of small circuit boards produced.
- $y$ as the number of large circuit boards produced.

The objective is to maximize profit. The profit from producing $x$ small circuit boards and $y$ large circuit boards can be calculated as $5x + 7y$, given that each small circuit board yields a profit of $5 and each large circuit board yields a profit of $7.

There are constraints based on the availability of time on both the drilling machine and the printing machine. For the drilling machine, each small circuit board requires 10 minutes, and each large circuit board requires 15 minutes. The total available time for the drilling machine is 600 minutes. This gives us our first constraint: $10x + 15y \leq 600$.

For the printing machine, each small circuit board takes 15 minutes, and each large circuit board takes 18 minutes, with a total of 600 minutes available. Thus, our second constraint is: $15x + 18y \leq 600$.

Additionally, we know that the number of circuit boards cannot be negative, so $x \geq 0$ and $y \geq 0$.

Now, let's translate this into Gurobi code in Python:

```python
from gurobipy import *

# Create a new model
m = Model("Circuit_Boards")

# Define variables
x = m.addVar(vtype=GRB.CONTINUOUS, name="small_circuit_boards", lb=0)
y = m.addVar(vtype=GRB.CONTINUOUS, name="large_circuit_boards", lb=0)

# Set the objective function: maximize profit
m.setObjective(5*x + 7*y, GRB.MAXIMIZE)

# Add constraints
m.addConstr(10*x + 15*y <= 600, "drilling_machine_time")
m.addConstr(15*x + 18*y <= 600, "printing_machine_time")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Small Circuit Boards: {x.x}")
    print(f"Large Circuit Boards: {y.x}")
    print(f"Maximum Profit: ${5*x.x + 7*y.x:.2f}")
else:
    print("No optimal solution found.")
```