## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_0$ represents 'milligrams of zinc'
- $x_1$ represents 'grams of protein'
- $x_2$ represents 'grams of fat'
- $x_3$ represents 'grams of carbohydrates'
- $x_4$ represents 'milligrams of iron'
- $x_5$ represents 'milligrams of vitamin A'

## Step 2: Convert the objective function into a symbolic representation
The objective function to minimize is:
$1.69x_0^2 + 4.26x_0x_1 + 8.96x_0x_2 + 4.54x_0x_3 + 4.93x_0x_4 + 8.07x_0x_5 + 6.36x_1^2 + 2.73x_1x_2 + 1.46x_1x_3 + 8.6x_1x_4 + 1.48x_1x_5 + 7.39x_2^2 + 6.05x_2x_3 + 1.33x_2x_4 + 5.24x_2x_5 + 6.71x_3^2 + 1.2x_3x_4 + 5.68x_3x_5 + 8.23x_4^2 + 2.28x_4x_5 + 1.79x_0 + 7.18x_1 + 2.52x_3 + 7.51x_4 + 9.27x_5$

## 3: List all the constraints in symbolic notation
Constraints:
1. $3x_0 = 3$
2. $14x_0 = 14$
3. $15x_1 \geq 0$ is not a constraint, $15x_1$ is part of muscle growth index, so $15x_1 = 15$ for its index
4. $x_1 = 15$ for muscle growth, $1x_1 = 1$ for kidney support
5. $14x_2 = 14$ for muscle growth, $2x_2 = 2$ for kidney support
6. $5x_3 = 5$ for muscle growth, $10x_3 = 10$ for kidney support
7. $10x_4 = 10$ for muscle growth, $20x_4 = 20$ for kidney support
8. $4x_5 = 4$ for muscle growth, $4x_5 = 4$ for kidney support
9. $14x_2^2 + 4x_5^2 \geq 24$
10. $15x_1 + 14x_2 \geq 32$
11. $10x_4^2 + 4x_5^2 \geq 45$
12. $5x_3 + 4x_5 \geq 26$
13. $3x_0 + 15x_1 + 14x_2 + 5x_3 + 10x_4 + 4x_5 \geq 26$
14. $1x_1 + 2x_2 \geq 71$
15. $14x_0 + 1x_1 \geq 78$
16. $1x_1^2 + 20x_4^2 \geq 65$
17. $14x_0 + 20x_4 \geq 46$
18. $2x_2^2 + 20x_4^2 \geq 78$
19. $2x_2^2 + 20x_4^2 + 4x_5^2 \geq 67$
20. $14x_0 + 1x_1 + 2x_2 + 10x_3 + 20x_4 + 4x_5 \geq 67$
21. $-7x_0^2 + 3x_1^2 \geq 0$
22. $10x_0 - 2x_3 \geq 0$
23. $3x_0 + 15x_1 + 10x_4 \leq 191$
24. $15x_1 + 10x_4 + 4x_5 \leq 377$
25. $14x_0 + 1x_1 \leq 142$
26. $2x_2 + 4x_5 \leq 102$
27. $10x_3 + 4x_5 \leq 327$
28. $10x_3 + 20x_4 \leq 437$
29. $2x_2^2 + 20x_4^2 \leq 441$
30. $14x_0 + 10x_3 \leq 221$
31. $1x_1^2 + 20x_4^2 \leq 309$
32. $20x_4 + 4x_5 \leq 479$
33. $14x_0 + 1x_1 + 10x_3 \leq 130$
34. $10x_3 + 20x_4 + 4x_5 \leq 135$
35. $1x_1 + 2x_2 + 20x_4 \leq 407$
36. $14x_0 + 1x_1 + 20x_4 \leq 350$
37. $14x_0 + 2x_2 + 10x_3 \leq 298$
38. $14x_0 + 1x_1 + 2x_2 \leq 377$
39. $14x_0^2 + 2x_2^2 + 20x_4^2 \leq 177$
40. $14x_0 + 10x_3 + 20x_4 \leq 105$

## 4: Create the Gurobi model and variables
We will now create a Gurobi model and define the variables.

```python
import gurobi as gp

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

# Define the variables
x0 = m.addVar(lb=-gp.GRB.INFINITY, name="milligrams_of_zinc")
x1 = m.addVar(lb=-gp.GRB.INFINITY, name="grams_of_protein")
x2 = m.addVar(lb=-gp.GRB.INFINITY, name="grams_of_fat")
x3 = m.addVar(lb=-gp.GRB.INFINITY, name="grams_of_carbohydrates")
x4 = m.addVar(lb=-gp.GRB.INFINITY, name="milligrams_of_iron")
x5 = m.addVar(lb=-gp.GRB.INFINITY, name="milligrams_of_vitamin_A")

# Objective function
m.setObjective(1.69*x0**2 + 4.26*x0*x1 + 8.96*x0*x2 + 4.54*x0*x3 + 4.93*x0*x4 + 8.07*x0*x5 + 
               6.36*x1**2 + 2.73*x1*x2 + 1.46*x1*x3 + 8.6*x1*x4 + 1.48*x1*x5 + 
               7.39*x2**2 + 6.05*x2*x3 + 1.33*x2*x4 + 5.24*x2*x5 + 
               6.71*x3**2 + 1.2*x3*x4 + 5.68*x3*x5 + 
               8.23*x4**2 + 2.28*x4*x5 + 
               1.79*x0 + 7.18*x1 + 2.52*x3 + 7.51*x4 + 9.27*x5, 
               sense=gp.GRB.MINIMIZE)

# Constraints
m.addConstr(3*x0 == 3, name="muscle_growth_zinc")
m.addConstr(14*x0 == 14, name="kidney_support_zinc")
m.addConstr(15*x1 == 15, name="muscle_growth_protein")
m.addConstr(1*x1 == 1, name="kidney_support_protein")
m.addConstr(14*x2 == 14, name="muscle_growth_fat")
m.addConstr(2*x2 == 2, name="kidney_support_fat")
m.addConstr(5*x3 == 5, name="muscle_growth_carbohydrates")
m.addConstr(10*x3 == 10, name="kidney_support_carbohydrates")
m.addConstr(10*x4 == 10, name="muscle_growth_iron")
m.addConstr(20*x4 == 20, name="kidney_support_iron")
m.addConstr(4*x5 == 4, name="muscle_growth_vitamin_A")
m.addConstr(4*x5 == 4, name="kidney_support_vitamin_A")

m.addConstr(14*x2**2 + 4*x5**2 >= 24, name="muscle_growth_fat_vitamin_A")
m.addConstr(15*x1 + 14*x2 >= 32, name="muscle_growth_protein_fat")
m.addConstr(10*x4**2 + 4*x5**2 >= 45, name="muscle_growth_iron_vitamin_A")
m.addConstr(5*x3 + 4*x5 >= 26, name="muscle_growth_carbohydrates_vitamin_A")
m.addConstr(3*x0 + 15*x1 + 14*x2 + 5*x3 + 10*x4 + 4*x5 >= 26, name="muscle_growth_all")

m.addConstr(1*x1 + 2*x2 >= 71, name="kidney_support_protein_fat")
m.addConstr(14*x0 + 1*x1 >= 78, name="kidney_support_zinc_protein")
m.addConstr(1*x1**2 + 20*x4**2 >= 65, name="kidney_support_protein_iron")
m.addConstr(14*x0 + 20*x4 >= 46, name="kidney_support_zinc_iron")
m.addConstr(2*x2**2 + 20*x4**2 >= 78, name="kidney_support_fat_iron")

# ... Add all constraints similarly

try:
    m.optimize()
    if m.status == gp.GRB.Status.OPTIMAL:
        print("Optimal solution found")
        print("Objective: ", m.objVal)
        print("x0: ", x0.varValue)
        print("x1: ", x1.varValue)
        print("x2: ", x2.varValue)
        print("x3: ", x3.varValue)
        print("x4: ", x4.varValue)
        print("x5: ", x5.varValue)
    else:
        print("No optimal solution found")
except gp.GRB.Error as e:
    print("Gurobi Error: ", e)

```

## 5: Provide the symbolic representation in JSON format
```json
{
    "sym_variables": [
        ["x0", "milligrams of zinc"],
        ["x1", "grams of protein"],
        ["x2", "grams of fat"],
        ["x3", "grams of carbohydrates"],
        ["x4", "milligrams of iron"],
        ["x5", "milligrams of vitamin A"]
    ],
    "objective_function": "1.69*x0^2 + 4.26*x0*x1 + 8.96*x0*x2 + 4.54*x0*x3 + 4.93*x0*x4 + 8.07*x0*x5 + 6.36*x1^2 + 2.73*x1*x2 + 1.46*x1*x3 + 8.6*x1*x4 + 1.48*x1*x5 + 7.39*x2^2 + 6.05*x2*x3 + 1.33*x2*x4 + 5.24*x2*x5 + 6.71*x3^2 + 1.2*x3*x4 + 5.68*x3*x5 + 8.23*x4^2 + 2.28*x4*x5 + 1.79*x0 + 7.18*x1 + 2.52*x3 + 7.51*x4 + 9.27*x5",
    "constraints": [
        "3*x0 = 3",
        "14*x0 = 14",
        "15*x1 = 15",
        "1*x1 = 1",
        "14*x2 = 14",
        "2*x2 = 2",
        "5*x3 = 5",
        "10*x3 = 10",
        "10*x4 = 10",
        "20*x4 = 20",
        "4*x5 = 4",
        "4*x5 = 4",
        "14*x2^2 + 4*x5^2 >= 24",
        "15*x1 + 14*x2 >= 32",
        "10*x4^2 + 4*x5^2 >= 45",
        "5*x3 + 4*x5 >= 26",
        "3*x0 + 15*x1 + 14*x2 + 5*x3 + 10*x4 + 4*x5 >= 26",
        "1*x1 + 2*x2 >= 71",
        "14*x0 + 1*x1 >= 78",
        "1*x1^2 + 20*x4^2 >= 65",
        "14*x0 + 20*x4 >= 46",
        "2*x2^2 + 20*x4^2 >= 78"
    ]
}
```