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

Let's define:
- $x_1$ as the number of bookcases produced in a week.
- $x_2$ as the number of coffee tables produced in a week.

The objective is to maximize profit. Given that the profit on a bookcase is $90 and on a coffee table is $65, the objective function can be written as:
\[ \text{Maximize:} \quad 90x_1 + 65x_2 \]

Now, let's formulate the constraints based on the given information:
1. The shop can make at most 40 bookcases in a week: $x_1 \leq 40$
2. The shop can make at most 60 coffee tables in a week: $x_2 \leq 60$
3. It takes 7 hours to make a bookcase and 5 hours to make a coffee table, with a total of at most 150 hours available per week: $7x_1 + 5x_2 \leq 150$

All variables should be non-negative since they represent quantities of products:
- $x_1 \geq 0$
- $x_2 \geq 0$

Therefore, the symbolic representation of the problem is:
```json
{
    'sym_variables': [('x1', 'number of bookcases'), ('x2', 'number of coffee tables')],
    'objective_function': '90*x1 + 65*x2',
    'constraints': ['x1 <= 40', 'x2 <= 60', '7*x1 + 5*x2 <= 150', 'x1 >= 0', 'x2 >= 0']
}
```

To solve this problem using Gurobi in Python, we'll use the following code:
```python
from gurobipy import *

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

# Define variables
x1 = m.addVar(lb=0, name="bookcases")
x2 = m.addVar(lb=0, name="coffee_tables")

# Set the objective function
m.setObjective(90*x1 + 65*x2, GRB.MAXIMIZE)

# Add constraints
m.addConstr(x1 <= 40, "max_bookcases")
m.addConstr(x2 <= 60, "max_coffee_tables")
m.addConstr(7*x1 + 5*x2 <= 150, "total_hours")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Bookcases: {x1.x}")
    print(f"Coffee tables: {x2.x}")
    print(f"Total profit: {m.objVal}")
else:
    print("No optimal solution found")
```