## Step 1: Define the symbolic representation of the problem
The problem involves two variables: 'bowls of cereal' and 'granola bars'. Let's denote 'bowls of cereal' as $x_1$ and 'granola bars' as $x_2$. The objective function to minimize is $8.94x_1^2 + 9.03x_1x_2 + 6.24x_1 + 1.28x_2$.

## Step 2: List the constraints in symbolic notation
The constraints are as follows:
1. $15x_1$ (cost of bowls of cereal)
2. $12x_1$ (iron from bowls of cereal)
3. $10x_2$ (cost of granola bars)
4. $22x_2$ (iron from granola bars)
5. $x_1^2 + x_2^2 \geq 34$ (minimum spend on bowls of cereal and granola bars squared)
6. $15x_1 + 10x_2 \geq 34$ (minimum spend on bowls of cereal and granola bars)
7. $12x_1^2 + 22x_2^2 \geq 53$ (minimum iron from bowls of cereal and granola bars squared)
8. $12x_1 + 22x_2 \geq 53$ (minimum iron from bowls of cereal and granola bars)
9. $-9x_1 + 10x_2 \geq 0$ (relationship between bowls of cereal and granola bars)
10. $15x_1 + 10x_2 \leq 90$ (maximum spend on bowls of cereal and granola bars)
11. $12x_1 + 22x_2 \leq 107$ (maximum iron from bowls of cereal and granola bars)
12. $x_1$ is an integer (whole number of bowls of cereal)
13. $x_2$ can be a non-integer (granola bars)

## 3: Convert the problem into a Gurobi-compatible format
We need to minimize $8.94x_1^2 + 9.03x_1x_2 + 6.24x_1 + 1.28x_2$ subject to the given constraints.

## 4: Write the Gurobi code
```python
import gurobi

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

# Define the variables
x1 = model.addVar(name="bowls_of_cereal", vtype=gurobi.GRB.INTEGER)  # integer variable for bowls of cereal
x2 = model.addVar(name="granola_bars")  # continuous variable for granola bars

# Objective function
model.setObjective(8.94 * x1**2 + 9.03 * x1 * x2 + 6.24 * x1 + 1.28 * x2, gurobi.GRB.MINIMIZE)

# Constraints
model.addConstr(15 * x1 <= 121, name="max_cost_bowls")  # assuming an upper bound for cost of bowls of cereal
model.addConstr(10 * x2 <= 113, name="max_cost_granola")  # assuming an upper bound for cost of granola bars
model.addConstr(15 * x1 + 10 * x2 >= 34, name="min_spend")
model.addConstr(x1**2 + x2**2 >= 34, name="min_spend_squared")
model.addConstr(12 * x1 + 22 * x2 >= 53, name="min_iron")
model.addConstr(12 * x1**2 + 22 * x2**2 >= 53, name="min_iron_squared")
model.addConstr(-9 * x1 + 10 * x2 >= 0, name="relationship")
model.addConstr(15 * x1 + 10 * x2 <= 90, name="max_spend")
model.addConstr(12 * x1 + 22 * x2 <= 107, name="max_iron")

# Optimize the model
model.optimize()

# Print the solution
if model.status == gurobi.GRB.OPTIMAL:
    print("Objective: ", model.objval)
    print("Bowls of cereal: ", x1.varValue)
    print("Granola bars: ", x2.varValue)
else:
    print("The model is infeasible")
```

## 5: Provide the symbolic representation of the problem
```json
{
    'sym_variables': [('x1', 'bowls of cereal'), ('x2', 'granola bars')],
    'objective_function': '8.94*x1^2 + 9.03*x1*x2 + 6.24*x1 + 1.28*x2',
    'constraints': [
        '15*x1 <= 121',
        '10*x2 <= 113',
        '15*x1 + 10*x2 >= 34',
        'x1^2 + x2^2 >= 34',
        '12*x1 + 22*x2 >= 53',
        '12*x1^2 + 22*x2^2 >= 53',
        '-9*x1 + 10*x2 >= 0',
        '15*x1 + 10*x2 <= 90',
        '12*x1 + 22*x2 <= 107',
        'x1 is an integer'
    ]
}
```