## Step 1: Define the variables and their corresponding symbolic notation
Let's denote the variables as follows:
- $x_0$ : bowls of cereal
- $x_1$ : peanutbutter sandwiches
- $x_2$ : apples
- $x_3$ : rotisserie chickens
- $x_4$ : oreos

## Step 2: Formulate the objective function
The objective function to minimize is $5x_0 + x_1 + 6x_2 + 9x_3 + 7x_4$.

## 3: Define the resources/attributes
Given resources/attributes:
- $r_0$ (sourness index) with upper bound 171
- $r_1$ (umami index) with upper bound 228

## 4: List the coefficients for sourness and umami indices
Sourness indices: $x_0(0.12), x_1(1.75), x_2(1.66), x_3(0.18), x_4(1.88)$
Umami indices: $x_0(0.13), x_1(0.75), x_2(1.43), x_3(0.04), x_4(0.97)$

## 5: Formulate the constraints
Constraints:
1. $1.75x_1 + 1.88x_4 \geq 14$
2. $0.12x_0 + 1.88x_4 \geq 21$
3. $0.12x_0 + 0.18x_3 \geq 23$
4. $0.12x_0 + 1.75x_1 \geq 32$
5. $1.66x_2 + 0.18x_3 + 1.88x_4 \geq 33$
6. $0.12x_0 + 1.75x_1 + 1.66x_2 + 0.18x_3 + 1.88x_4 \geq 33$
7. $0.13x_0 + 0.97x_4 \geq 42$
8. $0.04x_3 + 0.97x_4 \geq 35$
9. $1.43x_2 + 0.04x_3 \geq 35$
10. $0.75x_1 + 0.97x_4 \geq 31$
11. $0.13x_0 + 0.04x_3 + 0.97x_4 \geq 44$
12. $0.13x_0 + 0.75x_1 + 1.43x_2 \geq 44$
13. $0.13x_0 + 0.04x_3 + 0.97x_4 \geq 42$
14. $0.13x_0 + 0.75x_1 + 1.43x_2 \geq 42$
15. $0.13x_0 + 0.75x_1 + 1.43x_2 + 0.04x_3 + 0.97x_4 \geq 42$
16. $5x_2 - 6x_3 \geq 0$
17. $-5x_1 + x_3 \geq 0$
18. $10x_0 + 10x_3 - 4x_4 \geq 0$
19. $0.12x_0 + 1.88x_4 \leq 110$
20. $1.75x_1 + 0.18x_3 + 1.88x_4 \leq 89$
21. $1.75x_1 + 1.66x_2 + 0.18x_3 \leq 166$
22. $1.75x_1 + 1.66x_2 + 1.88x_4 \leq 50$
23. $0.12x_0 + 1.75x_1 + 0.18x_3 \leq 55$
24. $0.12x_0 + 1.66x_2 + 1.88x_4 \leq 74$
25. $0.13x_0 + 0.75x_1 + 0.97x_4 \leq 226$
26. $0.75x_1 + 1.43x_2 + 0.97x_4 \leq 196$
27. $0.13x_0 + 0.04x_3 + 0.97x_4 \leq 82$
28. $1.43x_2 + 0.04x_3 + 0.97x_4 \leq 152$

## 6: Symbolic Representation
```json
{
    'sym_variables': [
        ('x0', 'bowls of cereal'),
        ('x1', 'peanutbutter sandwiches'),
        ('x2', 'apples'),
        ('x3', 'rotisserie chickens'),
        ('x4', 'oreos')
    ],
    'objective_function': '5*x0 + x1 + 6*x2 + 9*x3 + 7*x4',
    'constraints': [
        '1.75*x1 + 1.88*x4 >= 14',
        '0.12*x0 + 1.88*x4 >= 21',
        '0.12*x0 + 0.18*x3 >= 23',
        '0.12*x0 + 1.75*x1 >= 32',
        '1.66*x2 + 0.18*x3 + 1.88*x4 >= 33',
        '0.12*x0 + 1.75*x1 + 1.66*x2 + 0.18*x3 + 1.88*x4 >= 33',
        '0.13*x0 + 0.97*x4 >= 42',
        '0.04*x3 + 0.97*x4 >= 35',
        '1.43*x2 + 0.04*x3 >= 35',
        '0.75*x1 + 0.97*x4 >= 31',
        '0.13*x0 + 0.04*x3 + 0.97*x4 >= 44',
        '0.13*x0 + 0.75*x1 + 1.43*x2 >= 44',
        '0.13*x0 + 0.04*x3 + 0.97*x4 >= 42',
        '0.13*x0 + 0.75*x1 + 1.43*x2 >= 42',
        '0.13*x0 + 0.75*x1 + 1.43*x2 + 0.04*x3 + 0.97*x4 >= 42',
        '5*x2 - 6*x3 >= 0',
        '-5*x1 + x3 >= 0',
        '10*x0 + 10*x3 - 4*x4 >= 0',
        '0.12*x0 + 1.88*x4 <= 110',
        '1.75*x1 + 0.18*x3 + 1.88*x4 <= 89',
        '1.75*x1 + 1.66*x2 + 0.18*x3 <= 166',
        '1.75*x1 + 1.66*x2 + 1.88*x4 <= 50',
        '0.12*x0 + 1.75*x1 + 0.18*x3 <= 55',
        '0.12*x0 + 1.66*x2 + 1.88*x4 <= 74',
        '0.13*x0 + 0.75*x1 + 0.97*x4 <= 226',
        '0.75*x1 + 1.43*x2 + 0.97*x4 <= 196',
        '0.13*x0 + 0.04*x3 + 0.97*x4 <= 82',
        '1.43*x2 + 0.04*x3 + 0.97*x4 <= 152'
    ]
}
```

## 7: Gurobi Code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x0")  # bowls of cereal
    x1 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x1")  # peanutbutter sandwiches
    x2 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x2")  # apples
    x3 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x3")  # rotisserie chickens
    x4 = model.addVar(lb=-gurobi.GRB.INFINITY, name="x4")  # oreos

    # Objective function
    model.setObjective(5 * x0 + x1 + 6 * x2 + 9 * x3 + 7 * x4, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(1.75 * x1 + 1.88 * x4 >= 14)
    model.addConstr(0.12 * x0 + 1.88 * x4 >= 21)
    model.addConstr(0.12 * x0 + 0.18 * x3 >= 23)
    model.addConstr(0.12 * x0 + 1.75 * x1 >= 32)
    model.addConstr(1.66 * x2 + 0.18 * x3 + 1.88 * x4 >= 33)
    model.addConstr(0.12 * x0 + 1.75 * x1 + 1.66 * x2 + 0.18 * x3 + 1.88 * x4 >= 33)
    model.addConstr(0.13 * x0 + 0.97 * x4 >= 42)
    model.addConstr(0.04 * x3 + 0.97 * x4 >= 35)
    model.addConstr(1.43 * x2 + 0.04 * x3 >= 35)
    model.addConstr(0.75 * x1 + 0.97 * x4 >= 31)
    model.addConstr(0.13 * x0 + 0.04 * x3 + 0.97 * x4 >= 44)
    model.addConstr(0.13 * x0 + 0.75 * x1 + 1.43 * x2 >= 44)
    model.addConstr(0.13 * x0 + 0.04 * x3 + 0.97 * x4 >= 42)
    model.addConstr(0.13 * x0 + 0.75 * x1 + 1.43 * x2 >= 42)
    model.addConstr(0.13 * x0 + 0.75 * x1 + 1.43 * x2 + 0.04 * x3 + 0.97 * x4 >= 42)
    model.addConstr(5 * x2 - 6 * x3 >= 0)
    model.addConstr(-5 * x1 + x3 >= 0)
    model.addConstr(10 * x0 + 10 * x3 - 4 * x4 >= 0)
    model.addConstr(0.12 * x0 + 1.88 * x4 <= 110)
    model.addConstr(1.75 * x1 + 0.18 * x3 + 1.88 * x4 <= 89)
    model.addConstr(1.75 * x1 + 1.66 * x2 + 0.18 * x3 <= 166)
    model.addConstr(1.75 * x1 + 1.66 * x2 + 1.88 * x4 <= 50)
    model.addConstr(0.12 * x0 + 1.75 * x1 + 0.18 * x3 <= 55)
    model.addConstr(0.12 * x0 + 1.66 * x2 + 1.88 * x4 <= 74)
    model.addConstr(0.13 * x0 + 0.75 * x1 + 0.97 * x4 <= 226)
    model.addConstr(0.75 * x1 + 1.43 * x2 + 0.97 * x4 <= 196)
    model.addConstr(0.13 * x0 + 0.04 * x3 + 0.97 * x4 <= 82)
    model.addConstr(1.43 * x2 + 0.04 * x3 + 0.97 * x4 <= 152)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"x0: {x0.varValue}")
        print(f"x1: {x1.varValue}")
        print(f"x2: {x2.varValue}")
        print(f"x3: {x3.varValue}")
        print(f"x4: {x4.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("No optimal solution found.")

solve_optimization_problem()
```