To solve the optimization problem described, we first need to translate the natural language description into a symbolic representation. This involves defining variables and formulating the objective function and constraints algebraically.

Let's define:
- $x_1$ as the number of cutting boards produced in a week.
- $x_2$ as the number of knife handles produced in a week.

The objective is to maximize profit. Given that the profit on a cutting board is $100 and on a knife handle is $250, the objective function can be written as:
\[ \text{Maximize:} \quad 100x_1 + 250x_2 \]

The constraints based on the problem description are:
1. The shop can make at most 30 cutting boards in a week: $x_1 \leq 30$.
2. The shop can make at most 50 knife handles in a week: $x_2 \leq 50$.
3. It takes 5 hours to make a cutting board and 10 hours to make a knife handle, with a total of at most 200 hours available per week: $5x_1 + 10x_2 \leq 200$.

Symbolic representation in JSON format:
```json
{
  'sym_variables': [('x1', 'number of cutting boards'), ('x2', 'number of knife handles')],
  'objective_function': '100*x1 + 250*x2',
  'constraints': ['x1 <= 30', 'x2 <= 50', '5*x1 + 10*x2 <= 200']
}
```

Now, let's write the Gurobi code in Python to solve this linear programming problem:

```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="cutting_boards")
x2 = m.addVar(lb=0, vtype=GRB.CONTINUOUS, name="knife_handles")

# Set the objective function
m.setObjective(100*x1 + 250*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 30, "max_cutting_boards")
m.addConstr(x2 <= 50, "max_knife_handles")
m.addConstr(5*x1 + 10*x2 <= 200, "total_hours")

# Optimize the model
m.optimize()

# Print the results
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Cutting Boards: {x1.x}")
    print(f"Knife Handles: {x2.x}")
    print(f"Total Profit: ${100*x1.x + 250*x2.x:.2f}")
else:
    print("No optimal solution found")
```