## Step 1: Define the symbolic representation of the variables
The variables are 'bowls of cereal', 'bowls of instant ramen', and 'tomatoes', 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 minimize is $3 \times \text{bowls of cereal} + 3 \times \text{bowls of instant ramen} + 7 \times \text{tomatoes}$, which in symbolic terms is $3x_0 + 3x_1 + 7x_2$.

## 3: List the constraints in symbolic notation
1. $\text{umami index of bowls of cereal} = 11x_0$
2. $\text{grams of protein in bowls of cereal} = 18x_0$
3. The umami index of bowls of instant ramen is $13x_1$.
4. $\text{grams of protein in bowls of instant ramen} = 5x_1$
5. The umami index of tomatoes is $24x_2$.
6. $\text{grams of protein in tomatoes} = 8x_2$.
7. $11x_0 + 13x_1 \geq 108$
8. $11x_0 + 24x_2 \geq 90$
9. $11x_0 + 13x_1 + 24x_2 \geq 90$
10. $18x_0 + 5x_1 \geq 42$
11. $18x_0 + 8x_2 \geq 67$
12. $5x_1 + 8x_2 \geq 106$
13. $18x_0 + 5x_1 + 8x_2 \geq 63$
14. $-2x_0 + 6x_2 \geq 0$
15. $9x_0 - 2x_1 \geq 0$
16. $11x_0 + 13x_1 \leq 448$ and also $11x_0 + 13x_1 \leq 319$ which seems to be a repetition or error, we consider $11x_0 + 13x_1 \leq 319$
17. $11x_0 + 24x_2 \leq 303$

## 4: Create a symbolic representation of the problem
```json
{
'sym_variables': [('x0', 'bowls of cereal'), ('x1', 'bowls of instant ramen'), ('x2', 'tomatoes')],
'objective_function': '3*x0 + 3*x1 + 7*x2',
'constraints': [
    '11*x0 + 13*x1 >= 108',
    '11*x0 + 24*x2 >= 90',
    '11*x0 + 13*x1 + 24*x2 >= 90',
    '18*x0 + 5*x1 >= 42',
    '18*x0 + 8*x2 >= 67',
    '5*x1 + 8*x2 >= 106',
    '18*x0 + 5*x1 + 8*x2 >= 63',
    '-2*x0 + 6*x2 >= 0',
    '9*x0 - 2*x1 >= 0',
    '11*x0 + 13*x1 <= 319',
    '11*x0 + 24*x2 <= 303'
]
}
```

## 5: Implement the optimization problem using Gurobi
```python
import gurobipy as gp

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

# Define the variables
x0 = m.addVar(name="bowls_of_cereal", lb=-gp.GRB.INFINITY)
x1 = m.addVar(name="bowls_of_instant_ramen", lb=-gp.GRB.INFINITY)
x2 = m.addVar(name="tomatoes", lb=-gp.GRB.INFINITY)

# Define the objective function
m.setObjective(3*x0 + 3*x1 + 7*x2, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(11*x0 + 13*x1 >= 108)
m.addConstr(11*x0 + 24*x2 >= 90)
m.addConstr(11*x0 + 13*x1 + 24*x2 >= 90)
m.addConstr(18*x0 + 5*x1 >= 42)
m.addConstr(18*x0 + 8*x2 >= 67)
m.addConstr(5*x1 + 8*x2 >= 106)
m.addConstr(18*x0 + 5*x1 + 8*x2 >= 63)
m.addConstr(-2*x0 + 6*x2 >= 0)
m.addConstr(9*x0 - 2*x1 >= 0)
m.addConstr(11*x0 + 13*x1 <= 319)
m.addConstr(11*x0 + 24*x2 <= 303)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Bowls of cereal: {x0.varValue}")
    print(f"Bowls of instant ramen: {x1.varValue}")
    print(f"Tomatoes: {x2.varValue}")
    print(f"Objective function value: {m.objVal}")
else:
    print("No optimal solution found.")
```