## Step 1: Define the symbolic representation of the problem
The symbolic representation of the problem consists of pairs of variables in symbolic notation and their corresponding natural language objects, the objective function rendered as an algebraic term, and the list of semi-algebraic constraints.

## Step 2: List the variables and their corresponding symbolic notation
Let's denote the variables as follows:
- $x_1$ : milkshakes
- $x_2$ : eggs
- $x_3$ : sashimi
- $x_4$ : cornichons
- $x_5$ : blueberry pies
- $x_6$ : protein bars
- $x_7$ : strawberries

## Step 3: Write down the objective function using symbolic variables
The objective function to minimize is:
\[ 5x_1^2 + 8x_1x_3 + 4x_1x_4 + 8x_1x_6 + 4x_2x_6 + 4x_2x_7 + 7x_3x_4 + 9x_3x_7 + 5x_4^2 + 4x_4x_5 + 2x_4x_6 + 9x_5x_6 + 5x_5x_7 + 7x_6^2 + 3x_6x_7 + 9x_7^2 + x_1 + x_3 + 6x_4 + 5x_5 + 4x_6 + 6x_7 \]

## 4: List the constraints
Constraints include:
- $1.6x_1 + x_2 + 1.13x_2 + 1.77x_3 + 0.25x_4 + 1.87x_5 + 1.81x_6 + 1.62x_7 \geq 24$ (sourness index)
- $1.6x_1 + 1.81x_6 \geq 24$
- $1.13x_2 + 1.62x_7 \geq 23$
- $1.6x_1 + 1.13x_2 + 1.77x_3 + 0.25x_4 + 1.87x_5 + 1.81x_6 + 1.62x_7 \geq 23$
- $0.13x_1 + 1.49x_3 + 0.74x_5 \geq 40$
- $0.04x_2 + 1.49x_3 \geq 28$
- $0.13x_1 + 0.74x_5 \geq 29$
- $0.13x_1 + 0.68x_4 \geq 44$
- $0.68x_4 + 0.39x_6 \geq 49$
- $0.13x_1^2 + 0.04x_2^2 \geq 23$
- ... (many more constraints)

## 5: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x1', 'milkshakes'), 
        ('x2', 'eggs'), 
        ('x3', 'sashimi'), 
        ('x4', 'cornichons'), 
        ('x5', 'blueberry pies'), 
        ('x6', 'protein bars'), 
        ('x7', 'strawberries')
    ], 
    'objective_function': '5*x1^2 + 8*x1*x3 + 4*x1*x4 + 8*x1*x6 + 4*x2*x6 + 4*x2*x7 + 7*x3*x4 + 9*x3*x7 + 5*x4^2 + 4*x4*x5 + 2*x4*x6 + 9*x5*x6 + 5*x5*x7 + 7*x6^2 + 3*x6*x7 + 9*x7^2 + x1 + x3 + 6*x4 + 5*x5 + 4*x6 + 6*x7', 
    'constraints': [
        '1.6*x1 + 1.13*x2 + 1.77*x3 + 0.25*x4 + 1.87*x5 + 1.81*x6 + 1.62*x7 >= 23',
        '1.6*x1 + 1.81*x6 >= 24',
        '1.13*x2 + 1.62*x7 >= 23',
        '0.97*x1 + 0.63*x2 + 1.62*x3 + 0.3*x4 + 0.01*x5 + 1.09*x6 + 0.38*x7 <= 336',
        '0.13*x1 + 0.04*x2 + 1.49*x3 + 0.68*x4 + 0.74*x5 + 0.39*x6 + 1.84*x7 <= 362',
        '1.6*x1 + x2 + 1.13*x2 + 1.77*x3 + 0.25*x4 + 1.87*x5 + 1.81*x6 + 1.62*x7 >= 24'
    ]
}
```

## 6: Implement the optimization problem using Gurobi
```python
import gurobi as gp

# Define the model
m = gp.Model()

# Define the variables
x1 = m.addVar(name="milkshakes", lb=0)
x2 = m.addVar(name="eggs", lb=0)
x3 = m.addVar(name="sashimi", lb=0)
x4 = m.addVar(name="cornichons", lb=0)
x5 = m.addVar(name="blueberry_pies", lb=0)
x6 = m.addVar(name="protein_bars", lb=0)
x7 = m.addVar(name="strawberries", lb=0)

# Objective function
m.setObjective(5*x1**2 + 8*x1*x3 + 4*x1*x4 + 8*x1*x6 + 4*x2*x6 + 4*x2*x7 + 7*x3*x4 + 9*x3*x7 + 5*x4**2 + 4*x4*x5 + 2*x4*x6 + 9*x5*x6 + 5*x5*x7 + 7*x6**2 + 3*x6*x7 + 9*x7**2 + x1 + x3 + 6*x4 + 5*x5 + 4*x6 + 6*x7, gp.GRB.MINIMIZE)

# Constraints
# Sourness index constraints
m.addConstr(1.6*x1 + 1.13*x2 + 1.77*x3 + 0.25*x4 + 1.87*x5 + 1.81*x6 + 1.62*x7 >= 23, name="sourness_index")
m.addConstr(1.6*x1 + 1.81*x6 >= 24, name="sourness_milkshakes_protein_bars")
m.addConstr(1.13*x2 + 1.62*x7 >= 23, name="sourness_eggs_strawberries")

# Fat constraints
m.addConstr(0.13*x1 + 1.49*x3 + 0.74*x5 >= 40, name="fat_sashimi_blueberry_pies")
m.addConstr(0.04*x2 + 1.49*x3 >= 28, name="fat_eggs_sashimi")
m.addConstr(0.13*x1 + 0.74*x5 >= 29, name="fat_milkshakes_blueberry_pies")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("Milkshakes: ", x1.varValue)
    print("Eggs: ", x2.varValue)
    print("Sashimi: ", x3.varValue)
    print("Cornichons: ", x4.varValue)
    print("Blueberry pies: ", x5.varValue)
    print("Protein bars: ", x6.varValue)
    print("Strawberries: ", x7.varValue)
else:
    print("The model is infeasible or unbounded.")
```