## Step 1: Define the symbolic representation of the variables
The variables are 'bowls of cereal', 'pickles', and 'protein bars'. Let's denote them as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is $7x_0^2 + 4x_0x_1 + 3x_0x_2 + 9x_1^2 + 3x_1x_2 + 7x_2^2 + 2x_0 + 5x_1$.

## 3: Define the constraints in symbolic notation
- The umami index of bowls of cereal is $4x_0$.
- The cost of bowls of cereal is $21x_0$.
- The umami index of pickles is $21x_1$.
- The cost of pickles is $10x_1$.
- The umami index of protein bars is $19x_2$.
- The cost of protein bars is $14x_2$.
- The total combined umami index from bowls of cereal and pickles should be at least 59: $4x_0 + 21x_1 \geq 59$.
- However, the problem states the total combined umami index from bowls of cereal, pickles, and protein bars must be at least 59: $4x_0 + 21x_1 + 19x_2 \geq 59$.
- The total combined umami index from bowls of cereal squared and pickles squared should be 59 at a minimum: $(4x_0)^2 + (21x_1)^2 \geq 59$.
- You have to spend at least $73 on bowls of cereal squared plus pickles squared: $(21x_0)^2 + (10x_1)^2 \geq 73$.
- You have to spend at least $49 on pickles plus protein bars: $10x_1 + 14x_2 \geq 49$.
- You can spend no less than $49 on bowls of cereal plus pickles plus protein bars: $21x_0 + 10x_1 + 14x_2 \geq 49$.
- $9x_0 - 3x_2 \geq 0$.
- The total combined umami index from bowls of cereal plus pickles should be at most 133: $4x_0 + 21x_1 \leq 133$.
- You must spend no greater than $247 on bowls of cereal squared, pickles squared, and protein bars squared: $(21x_0)^2 + (10x_1)^2 + (14x_2)^2 \leq 247$.

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [
    ('x0', 'bowls of cereal'), 
    ('x1', 'pickles'), 
    ('x2', 'protein bars')
],
'objective_function': '7*x0^2 + 4*x0*x1 + 3*x0*x2 + 9*x1^2 + 3*x1*x2 + 7*x2^2 + 2*x0 + 5*x1',
'constraints': [
    '4*x0 <= 195',
    '21*x0 <= 446',
    '21*x1 <= 446',
    '10*x1 <= 446',
    '19*x2 <= 446',
    '14*x2 <= 446',
    '(4*x0)^2 + (21*x1)^2 >= 59',
    '4*x0 + 21*x1 + 19*x2 >= 59',
    '(21*x0)^2 + (10*x1)^2 >= 73',
    '10*x1 + 14*x2 >= 49',
    '21*x0 + 10*x1 + 14*x2 >= 49',
    '9*x0 - 3*x2 >= 0',
    '4*x0 + 21*x1 <= 133',
    '(21*x0)^2 + (10*x1)^2 + (14*x2)^2 <= 247',
    'x1 % 1 == 0',  # x1 is an integer
    'x2 % 1 == 0'   # x2 is an integer
]
}
```

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

def solve_optimization_problem():
    model = gurobi.Model()

    # Define variables
    x0 = model.addVar(name="bowls_of_cereal", lb=-gurobi.GRB.INFINITY, ub=gurobi.GRB.INFINITY)
    x1 = model.addVar(name="pickles", lb=0, ub=gurobi.GRB.INFINITY, vtype=gurobi.GRB.INTEGER)
    x2 = model.addVar(name="protein_bars", lb=0, ub=gurobi.GRB.INFINITY, vtype=gurobi.GRB.INTEGER)

    # Objective function
    model.setObjective(7*x0**2 + 4*x0*x1 + 3*x0*x2 + 9*x1**2 + 3*x1*x2 + 7*x2**2 + 2*x0 + 5*x1, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(4*x0 <= 195, name="umami_index_cereal")
    model.addConstr(21*x0 <= 446, name="cost_cereal")
    model.addConstr(21*x1 <= 446, name="cost_pickles")
    model.addConstr(10*x1 <= 446, name="cost_pickles2")
    model.addConstr(19*x2 <= 446, name="umami_index_protein_bars")
    model.addConstr(14*x2 <= 446, name="cost_protein_bars")
    model.addConstr((4*x0)**2 + (21*x1)**2 >= 59, name="min_umami_index_cereal_pickles")
    model.addConstr(4*x0 + 21*x1 + 19*x2 >= 59, name="min_umami_index_all")
    model.addConstr((21*x0)**2 + (10*x1)**2 >= 73, name="min_cost_cereal_pickles")
    model.addConstr(10*x1 + 14*x2 >= 49, name="min_cost_pickles_protein_bars")
    model.addConstr(21*x0 + 10*x1 + 14*x2 >= 49, name="min_cost_all")
    model.addConstr(9*x0 - 3*x2 >= 0, name="cereal_protein_bars_constraint")
    model.addConstr(4*x0 + 21*x1 <= 133, name="max_umami_index_cereal_pickles")
    model.addConstr((21*x0)**2 + (10*x1)**2 + (14*x2)**2 <= 247, name="max_cost_all")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("bowls of cereal: ", x0.varValue)
        print("pickles: ", x1.varValue)
        print("protein bars: ", x2.varValue)
    else:
        print("The model is infeasible")

solve_optimization_problem()
```