## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'milkshakes' and 'peanutbutter sandwiches', which we can denote as $x_1$ and $x_2$ respectively. The objective function to maximize is $1.66x_1 + 8.63x_2$. The constraints are:
- $8.76x_1 + 11.41x_2 \geq 36$
- $x_1 - 9x_2 \geq 0$
- $8.76x_1 + 11.41x_2 \leq 58$
- $x_1, x_2$ can be fractional.

## Step 2: Convert the problem into a symbolic representation
The symbolic representation of the variables is:
- $x_1$ represents 'milkshakes'
- $x_2$ represents 'peanutbutter sandwiches'

The objective function in symbolic notation is: $1.66x_1 + 8.63x_2$

The constraints in symbolic notation are:
- $8.76x_1 + 11.41x_2 \geq 36$
- $x_1 - 9x_2 \geq 0$
- $8.76x_1 + 11.41x_2 \leq 58$

## 3: Express the problem in a format that can be used to verify the Gurobi code
```json
{
'sym_variables': [('x1', 'milkshakes'), ('x2', 'peanutbutter sandwiches')],
'objective_function': '1.66x1 + 8.63x2',
'constraints': [
    '8.76x1 + 11.41x2 >= 36',
    'x1 - 9x2 >= 0',
    '8.76x1 + 11.41x2 <= 58'
]
}
```

## 4: Write the Gurobi code to solve the optimization problem
```python
import gurobipy as gp

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

# Define the variables
milkshakes = model.addVar(name="milkshakes", lb=0)  # Assuming non-negative
peanutbutter_sandwiches = model.addVar(name="peanutbutter_sandwiches", lb=0)  # Assuming non-negative

# Define the objective function
model.setObjective(1.66 * milkshakes + 8.63 * peanutbutter_sandwiches, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(8.76 * milkshakes + 11.41 * peanutbutter_sandwiches >= 36)
model.addConstr(milkshakes - 9 * peanutbutter_sandwiches >= 0)
model.addConstr(8.76 * milkshakes + 11.41 * peanutbutter_sandwiches <= 58)

# Optimize the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print("Optimal Solution:")
    print(f"Milkshakes: {milkshakes.varValue}")
    print(f"Peanutbutter Sandwiches: {peanutbutter_sandwiches.varValue}")
    print(f"Objective Function Value: {model.objVal}")
else:
    print("The model is infeasible or unbounded.")
```