## Step 1: Define the symbolic representation of the variables
The variables are 'peanutbutter sandwiches', 'blueberry pies', and 'strawberries', which can be represented symbolically as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to maximize is $7x_0^2 + 3x_0x_1 + 8x_0x_2$.

## Step 3: List the constraints in symbolic notation
The constraints are:
- $2x_0 + 10x_1 + 5x_2 \leq 55$ (grams of fiber, total)
- $8x_0 + 5x_1 + 3x_2 \leq 59$ (milligrams of calcium, total)
- $2x_0 + 9x_1 + 4x_2 \leq 67$ (grams of carbohydrates, total)
- $8x_0 + 5x_1 + 3x_2 \geq 17$ (at least 17 milligrams of calcium)
- $2x_0 + 5x_2 \leq 41$ (at most 41 grams of fiber from peanutbutter sandwiches and strawberries)
- $2x_0 + 10x_1 \leq 49$ (up to 49 grams of fiber from peanutbutter sandwiches and blueberry pies)
- $2x_0 + 10x_1 + 5x_2 \leq 49$ (up to 49 grams of fiber from all)
- $8x_0 + 3x_2 \leq 50$ (no more than 50 milligrams of calcium from peanutbutter sandwiches and strawberries)
- $5x_1 + 3x_2 \leq 43$ (up to 43 milligrams of calcium from blueberry pies and strawberries)
- $8x_0 + 5x_1 + 3x_2 \leq 43$ (up to 43 milligrams of calcium from all)
- $9x_1^2 + 4x_2^2 \leq 45$ (no more than 45 grams of carbohydrates from blueberry pies squared and strawberries squared)
- $2x_0 + 4x_2 \leq 52$ (no more than 52 grams of carbohydrates from peanutbutter sandwiches and strawberries)
- $4x_0^2 + 9x_1^2 \leq 27$ (no more than 27 grams of carbohydrates from peanutbutter sandwiches squared and blueberry pies squared)
- $2x_0 + 9x_1 + 4x_2 \leq 27$ (no more than 27 grams of carbohydrates from all)

## Step 4: Create the symbolic representation of the problem
```json
{
    'sym_variables': [
        ('x0', 'peanutbutter sandwiches'), 
        ('x1', 'blueberry pies'), 
        ('x2', 'strawberries')
    ], 
    'objective_function': '7*x0^2 + 3*x0*x1 + 8*x0*x2', 
    'constraints': [
        '2*x0 + 10*x1 + 5*x2 <= 55',
        '8*x0 + 5*x1 + 3*x2 <= 59',
        '2*x0 + 9*x1 + 4*x2 <= 67',
        '8*x0 + 5*x1 + 3*x2 >= 17',
        '2*x0 + 5*x2 <= 41',
        '2*x0 + 10*x1 <= 49',
        '2*x0 + 10*x1 + 5*x2 <= 49',
        '8*x0 + 3*x2 <= 50',
        '5*x1 + 3*x2 <= 43',
        '8*x0 + 5*x1 + 3*x2 <= 43',
        '9*x1^2 + 4*x2^2 <= 45',
        '2*x0 + 4*x2 <= 52',
        '4*x0^2 + 9*x1^2 <= 27',
        '2*x0 + 9*x1 + 4*x2 <= 27'
    ]
}
```

## Step 5: Write the Gurobi code to solve the optimization problem
```python
import gurobi

# Create a new model
m = gurobi.Model()

# Define the variables
x0 = m.addVar(name="peanutbutter_sandwiches", lb=0)  # lower bound is 0, no upper bound
x1 = m.addVar(name="blueberry_pies", lb=0)  # lower bound is 0, no upper bound
x2 = m.addVar(name="strawberries", lb=0)  # lower bound is 0, no upper bound

# Objective function
m.setObjective(7*x0**2 + 3*x0*x1 + 8*x0*x2, gurobi.GRB.MAXIMIZE)

# Constraints
m.addConstr(2*x0 + 10*x1 + 5*x2 <= 55)
m.addConstr(8*x0 + 5*x1 + 3*x2 <= 59)
m.addConstr(2*x0 + 9*x1 + 4*x2 <= 67)
m.addConstr(8*x0 + 5*x1 + 3*x2 >= 17)
m.addConstr(2*x0 + 5*x2 <= 41)
m.addConstr(2*x0 + 10*x1 <= 49)
m.addConstr(2*x0 + 10*x1 + 5*x2 <= 49)
m.addConstr(8*x0 + 3*x2 <= 50)
m.addConstr(5*x1 + 3*x2 <= 43)
m.addConstr(8*x0 + 5*x1 + 3*x2 <= 43)
m.addConstr(9*x1**2 + 4*x2**2 <= 45)
m.addConstr(2*x0 + 4*x2 <= 52)
m.addConstr(4*x0**2 + 9*x1**2 <= 27)
m.addConstr(2*x0 + 9*x1 + 4*x2 <= 27)

# Optimize the model
m.optimize()

# Print the solution
if m.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Peanutbutter sandwiches: ", x0.varValue)
    print("Blueberry pies: ", x1.varValue)
    print("Strawberries: ", x2.varValue)
else:
    print("The model is infeasible")
```