To solve the optimization problem described, we first need to convert the natural language description into a symbolic representation. This involves defining variables for the quantities of small and large circuit boards to be made, formulating the objective function that represents the total profit, and listing the constraints based on the time availability of the drilling and printing machines.

Let's denote:
- $x_1$ as the number of small circuit boards made,
- $x_2$ as the number of large circuit boards made.

The objective function aims to maximize the total profit. Given that each small circuit board yields a profit of $5 and each large circuit board yields a profit of $7, the objective function can be written as:
\[ \text{Maximize} \quad 5x_1 + 7x_2 \]

The constraints are based on the time availability of the machines:
- Each small circuit board takes 10 minutes on the drilling machine, and each large circuit board takes 15 minutes. The drilling machine is available for at most 600 minutes a day. Therefore, the constraint for the drilling machine can be written as:
\[ 10x_1 + 15x_2 \leq 600 \]
- Each small circuit board takes 15 minutes on the printing machine, and each large circuit board takes 18 minutes. The printing machine is also available for at most 600 minutes a day. Thus, the constraint for the printing machine can be written as:
\[ 15x_1 + 18x_2 \leq 600 \]
- Additionally, $x_1$ and $x_2$ must be non-negative since they represent quantities of circuit boards.

Therefore, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of small circuit boards'), ('x2', 'number of large circuit boards')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': ['10*x1 + 15*x2 <= 600', '15*x1 + 18*x2 <= 600', 'x1 >= 0', 'x2 >= 0']
}
```

Now, let's implement this problem using Gurobi in Python:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.INTEGER, name="small_circuit_boards")
x2 = m.addVar(lb=0, vtype=GRB.INTEGER, name="large_circuit_boards")

# Set the objective function
m.setObjective(5*x1 + 7*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(10*x1 + 15*x2 <= 600, "drilling_machine")
m.addConstr(15*x1 + 18*x2 <= 600, "printing_machine")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Number of small circuit boards: {x1.x}")
    print(f"Number of large circuit boards: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```