To solve the given optimization problem, we first need to translate the natural language description into a symbolic representation. This involves defining variables for the quantities of canoes and paddles to be made, formulating the objective function that represents the total profit, and listing the constraints based on the available time for each operation (cutting, woodworking, and sanding).

Let's define:
- \(x_1\) as the number of canoes to be made,
- \(x_2\) as the number of paddles to be made.

The objective function, which is to maximize profit, can be written as:
\[500x_1 + 75x_2\]

Given the time requirements and availability for each operation, we have the following constraints:
1. Cutting: \(1x_1 + 0.5x_2 \leq 80\)
2. Woodworking: \(5x_1 + 1x_2 \leq 100\)
3. Sanding: \(2x_1 + 0.75x_2 \leq 70\)

Also, since we cannot make a negative number of canoes or paddles, we have:
- \(x_1 \geq 0\)
- \(x_2 \geq 0\)

The symbolic representation in JSON format is:
```json
{
    'sym_variables': [('x1', 'number of canoes'), ('x2', 'number of paddles')],
    'objective_function': '500*x1 + 75*x2',
    'constraints': [
        '1*x1 + 0.5*x2 <= 80',
        '5*x1 + 1*x2 <= 100',
        '2*x1 + 0.75*x2 <= 70',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

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

```python
from gurobipy import *

# Create a new model
model = Model("Wood Shop Optimization")

# Define the variables
x1 = model.addVar(vtype=GRB.CONTINUOUS, name="canoes", lb=0)
x2 = model.addVar(vtype=GRB.CONTINUOUS, name="paddles", lb=0)

# Set the objective function
model.setObjective(500*x1 + 75*x2, GRB.MAXIMIZE)

# Add constraints
model.addConstr(x1 + 0.5*x2 <= 80, "cutting")
model.addConstr(5*x1 + x2 <= 100, "woodworking")
model.addConstr(2*x1 + 0.75*x2 <= 70, "sanding")

# Optimize the model
model.optimize()

# Print the results
if model.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Canoes: {x1.x}")
    print(f"Paddles: {x2.x}")
    print(f"Maximum Profit: ${model.objVal:.2f}")
else:
    print("No optimal solution found")
```