## Step 1: Define the symbolic representation of the variables
The variables are 'apple pies', 'protein bars', and 'bowls of instant ramen', which we will denote as $x_0$, $x_1$, and $x_2$ respectively.

## Step 2: Define the objective function in symbolic notation
The objective function to maximize is $1.21x_0^2 + 2.36x_0x_1 + 7.88x_0 + 2.72x_2$.

## Step 3: Define the constraints in symbolic notation
The constraints are:
- $1x_0 \leq 275$ (umami index of apple pies)
- $10x_0 \leq 391$ (grams of fat from apple pies)
- $19x_1 \geq 0$ (umami index of protein bars, always true)
- $18x_1 \geq 0$ (grams of fat from protein bars, always true)
- $19x_2 \geq 0$ (umami index of bowls of instant ramen, always true)
- $14x_2 \geq 0$ (grams of fat from bowls of instant ramen, always true)
- $19x_1 + 19x_2 \geq 86$ (total umami index from protein bars and bowls of instant ramen)
- $1x_0^2 + 19x_1^2 + 19x_2^2 \geq 45$ (total combined umami index squared)
- $18x_1 + 14x_2 \geq 99$ (total grams of fat from protein bars and bowls of instant ramen)
- $10x_0^2 + 14x_2^2 \geq 97$ (grams of fat from apple pies squared and bowls of instant ramen squared)
- $10x_0^2 + 18x_1^2 \geq 114$ (grams of fat from apple pies squared and protein bars squared)
- $1x_0^2 + 19x_1^2 \leq 200$ (total umami index from apple pies squared and protein bars squared)
- $1x_0^2 + 19x_2^2 \leq 168$ (total umami index from apple pies squared and bowls of instant ramen squared)
- $19x_1 + 19x_2 \leq 188$ (total umami index from protein bars and bowls of instant ramen)
- $1x_0 + 19x_1 + 19x_2 \leq 188$ (total umami index from all)
- $18x_1^2 + 14x_2^2 \leq 291$ (grams of fat from protein bars squared and bowls of instant ramen squared)
- $10x_0^2 + 18x_1^2 \leq 277$ (grams of fat from apple pies squared and protein bars squared)
- $10x_0 + 18x_1 + 14x_2 \leq 277$ (total grams of fat from all)

## Step 4: Convert the problem into Gurobi code
We will use Gurobi to solve this optimization problem.

```python
import gurobi as gp

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

# Define the variables
x0 = m.addVar(name="apple_pies", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)
x1 = m.addVar(name="protein_bars", lb=0, ub=gp.GRB.INFINITY, vtype=gp.GRB.INTEGER)
x2 = m.addVar(name="bowls_of_instant_ramen", lb=-gp.GRB.INFINITY, ub=gp.GRB.INFINITY)

# Define the objective function
m.setObjective(1.21*x0**2 + 2.36*x0*x1 + 7.88*x0 + 2.72*x2, gp.GRB.MAXIMIZE)

# Add constraints
m.addConstr(x0 <= 275)  # umami index of apple pies
m.addConstr(10*x0 <= 391)  # grams of fat from apple pies
m.addConstr(19*x1 + 19*x2 >= 86)  # total umami index from protein bars and bowls of instant ramen
m.addConstr(x0**2 + 19*x1**2 + 19*x2**2 >= 45)  # total combined umami index squared
m.addConstr(18*x1 + 14*x2 >= 99)  # total grams of fat from protein bars and bowls of instant ramen
m.addConstr(10*x0**2 + 14*x2**2 >= 97)  # grams of fat from apple pies squared and bowls of instant ramen squared
m.addConstr(10*x0**2 + 18*x1**2 >= 114)  # grams of fat from apple pies squared and protein bars squared
m.addConstr(x0**2 + 19*x1**2 <= 200)  # total umami index from apple pies squared and protein bars squared
m.addConstr(x0**2 + 19*x2**2 <= 168)  # total umami index from apple pies squared and bowls of instant ramen squared
m.addConstr(19*x1 + 19*x2 <= 188)  # total umami index from protein bars and bowls of instant ramen
m.addConstr(x0 + 19*x1 + 19*x2 <= 188)  # total umami index from all
m.addConstr(18*x1**2 + 14*x2**2 <= 291)  # grams of fat from protein bars squared and bowls of instant ramen squared
m.addConstr(10*x0**2 + 18*x1**2 <= 277)  # grams of fat from apple pies squared and protein bars squared
m.addConstr(10*x0 + 18*x1 + 14*x2 <= 277)  # total grams of fat from all

# Optimize the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Apple Pies: ", x0.varValue)
    print("Protein Bars: ", x1.varValue)
    print("Bowls of Instant Ramen: ", x2.varValue)
else:
    print("The model is infeasible")
```

## Step 5: Provide the symbolic representation of the problem
```json
{
    "sym_variables": [
        ["x0", "apple pies"],
        ["x1", "protein bars"],
        ["x2", "bowls of instant ramen"]
    ],
    "objective_function": "1.21*x0^2 + 2.36*x0*x1 + 7.88*x0 + 2.72*x2",
    "constraints": [
        "x0 <= 275",
        "10*x0 <= 391",
        "19*x1 + 19*x2 >= 86",
        "x0^2 + 19*x1^2 + 19*x2^2 >= 45",
        "18*x1 + 14*x2 >= 99",
        "10*x0^2 + 14*x2^2 >= 97",
        "10*x0^2 + 18*x1^2 >= 114",
        "x0^2 + 19*x1^2 <= 200",
        "x0^2 + 19*x2^2 <= 168",
        "19*x1 + 19*x2 <= 188",
        "x0 + 19*x1 + 19*x2 <= 188",
        "18*x1^2 + 14*x2^2 <= 291",
        "10*x0^2 + 18*x1^2 <= 277",
        "10*x0 + 18*x1 + 14*x2 <= 277"
    ]
}
```