## Symbolic Representation

To solve the given optimization problem, we first need to convert the natural language description into a symbolic representation.

Let's define the symbolic variables as follows:

- `x1`: Canoes
- `x2`: Paddles

The objective is to maximize profit. The profit per canoe is $500, and the profit per paddle is $75. Therefore, the objective function can be represented as:

`Maximize: 500*x1 + 75*x2`

The constraints based on the available time for each activity are:

- Cutting: `1*x1 + 0.5*x2 <= 80`
- Woodworking: `5*x1 + 1*x2 <= 100`
- Sanding: `2*x1 + 0.75*x2 <= 70`
- Non-negativity: `x1 >= 0, x2 >= 0`

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'Canoes'), ('x2', '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'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

# Create a new model
model = gp.Model("Canoe_and_Paddle_Production")

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

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

# Add constraints
model.addConstr(x1 + 0.5*x2 <= 80, name="cutting_constraint")  # Cutting constraint
model.addConstr(5*x1 + x2 <= 100, name="woodworking_constraint")  # Woodworking constraint
model.addConstr(2*x1 + 0.75*x2 <= 70, name="sanding_constraint")  # Sanding constraint

# Solve the model
model.optimize()

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