## Step 1: Define the symbolic representation of the variables
The variables are ['milligrams of vitamin B12', 'grams of protein', 'milligrams of zinc']. Let's denote them as $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Convert the natural language objects into symbolic notation
The symbolic representation of the variables is:
- $x_1$ : milligrams of vitamin B12
- $x_2$ : grams of protein
- $x_3$ : milligrams of zinc

## 3: Define the objective function in symbolic notation
The objective function to minimize is: $1.84x_1^2 + 6.46x_1x_2 + 4.61x_2^2 + 1.45x_2x_3 + 5.7x_1$.

## 4: List the constraints in symbolic notation
Constraints:
1. $19x_1 \leq 84$
2. $6x_1 \leq 107$
3. $5x_1 \leq 107$
4. $11x_1 \leq 83$
5. $8x_1 \leq 80$
6. $4x_2 \leq 84$
7. $14x_2 \leq 107$
8. $2x_2 \leq 107$
9. $20x_2 \leq 83$
10. $2x_2 \leq 80$
11. $6x_3 \leq 84$
12. $8x_3 \leq 107$
13. $2x_3 \leq 107$
14. $14x_3 \leq 83$
15. $20x_3 \leq 80$
16. $19x_1 + 4x_2 \geq 11$
17. $19x_1 + 6x_3 \geq 15$
18. $19x_1 + 4x_2 + 6x_3 \geq 15$
19. $6x_1 + 14x_2 \geq 17$
20. $6x_1 + 8x_3 \geq 26$
21. $6x_1^2 + 14x_2^2 + 8x_3^2 \geq 27$
22. $6x_1 + 14x_2 + 8x_3 \geq 27$
23. $5x_1 + 2x_3 \geq 30$
24. $5x_1 + 2x_2 \geq 33$
25. $2x_2 + 2x_3 \geq 24$
26. $5x_1 + 2x_2 + 2x_3 \geq 24$
27. $11x_1^2 + 20x_2^2 \geq 14$
28. $20x_2 + 14x_3 \geq 15$
29. $11x_1 + 14x_3 \geq 24$
30. $11x_1 + 20x_2 + 14x_3 \geq 24$
31. $8x_1 + 2x_2 \geq 21$
32. $8x_1 + 20x_3 \geq 23$
33. $2x_2 + 20x_3 \geq 16$
34. $8x_1 + 2x_2 + 20x_3 \geq 14$
35. $8x_1 + 2x_2 + 20x_3 \geq 14$
36. $-5x_1^2 + 7x_2^2 \geq 0$
37. $4x_2 + 6x_3 \leq 70$
38. $5x_1^2 + 2x_2^2 \leq 49$
39. $11x_1 + 14x_3 \leq 75$
40. $2x_2^2 + 20x_3^2 \leq 64$
41. $x_3 \geq 0$ and $x_3$ is an integer.

## 5: Write down the problem in a formal optimization problem statement
Minimize $1.84x_1^2 + 6.46x_1x_2 + 4.61x_2^2 + 1.45x_2x_3 + 5.7x_1$

Subject to:
- All constraints listed above.

## 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="milligrams_of_vitamin_B12", lb=-gp.GRB.INFINITY)
x2 = m.addVar(name="grams_of_protein", lb=-gp.GRB.INFINITY)
x3 = m.addVar(name="milligrams_of_zinc", lb=0, type=gp.GRB.INTEGER)

# Define the objective function
m.setObjective(1.84*x1**2 + 6.46*x1*x2 + 4.61*x2**2 + 1.45*x2*x3 + 5.7*x1, gp.GRB.MINIMIZE)

# Add constraints
m.addConstr(19*x1 <= 84)
m.addConstr(6*x1 <= 107)
m.addConstr(5*x1 <= 107)
m.addConstr(11*x1 <= 83)
m.addConstr(8*x1 <= 80)
m.addConstr(4*x2 <= 84)
m.addConstr(14*x2 <= 107)
m.addConstr(2*x2 <= 107)
m.addConstr(20*x2 <= 83)
m.addConstr(2*x2 <= 80)
m.addConstr(6*x3 <= 84)
m.addConstr(8*x3 <= 107)
m.addConstr(2*x3 <= 107)
m.addConstr(14*x3 <= 83)
m.addConstr(20*x3 <= 80)
m.addConstr(19*x1 + 4*x2 >= 11)
m.addConstr(19*x1 + 6*x3 >= 15)
m.addConstr(19*x1 + 4*x2 + 6*x3 >= 15)
m.addConstr(6*x1 + 14*x2 >= 17)
m.addConstr(6*x1 + 8*x3 >= 26)
m.addConstr(6*x1**2 + 14*x2**2 + 8*x3**2 >= 27)
m.addConstr(6*x1 + 14*x2 + 8*x3 >= 27)
m.addConstr(5*x1 + 2*x3 >= 30)
m.addConstr(5*x1 + 2*x2 >= 33)
m.addConstr(2*x2 + 2*x3 >= 24)
m.addConstr(5*x1 + 2*x2 + 2*x3 >= 24)
m.addConstr(11*x1**2 + 20*x2**2 >= 14)
m.addConstr(20*x2 + 14*x3 >= 15)
m.addConstr(11*x1 + 14*x3 >= 24)
m.addConstr(11*x1 + 20*x2 + 14*x3 >= 24)
m.addConstr(8*x1 + 2*x2 >= 21)
m.addConstr(8*x1 + 20*x3 >= 23)
m.addConstr(2*x2 + 20*x3 >= 16)
m.addConstr(8*x1 + 2*x2 + 20*x3 >= 14)
m.addConstr(-5*x1**2 + 7*x2**2 >= 0)
m.addConstr(4*x2 + 6*x3 <= 70)
m.addConstr(5*x1**2 + 2*x2**2 <= 49)
m.addConstr(11*x1 + 14*x3 <= 75)
m.addConstr(2*x2**2 + 20*x3**2 <= 64)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Milligrams of vitamin B12: ", x1.varValue)
    print("Grams of protein: ", x2.varValue)
    print("Milligrams of zinc: ", x3.varValue)
else:
    print("No optimal solution found.")
```

## 7: Symbolic representation of the problem
```json
{
    "sym_variables": [
        ["x1", "milligrams of vitamin B12"],
        ["x2", "grams of protein"],
        ["x3", "milligrams of zinc"]
    ],
    "objective_function": "1.84*x1^2 + 6.46*x1*x2 + 4.61*x2^2 + 1.45*x2*x3 + 5.7*x1",
    "constraints": [
        "19*x1 <= 84",
        "6*x1 <= 107",
        "5*x1 <= 107",
        "11*x1 <= 83",
        "8*x1 <= 80",
        "4*x2 <= 84",
        "14*x2 <= 107",
        "2*x2 <= 107",
        "20*x2 <= 83",
        "2*x2 <= 80",
        "6*x3 <= 84",
        "8*x3 <= 107",
        "2*x3 <= 107",
        "14*x3 <= 83",
        "20*x3 <= 80",
        "19*x1 + 4*x2 >= 11",
        "19*x1 + 6*x3 >= 15",
        "19*x1 + 4*x2 + 6*x3 >= 15",
        "6*x1 + 14*x2 >= 17",
        "6*x1 + 8*x3 >= 26",
        "6*x1^2 + 14*x2^2 + 8*x3^2 >= 27",
        "6*x1 + 14*x2 + 8*x3 >= 27",
        "5*x1 + 2*x3 >= 30",
        "5*x1 + 2*x2 >= 33",
        "2*x2 + 2*x3 >= 24",
        "5*x1 + 2*x2 + 2*x3 >= 24",
        "11*x1^2 + 20*x2^2 >= 14",
        "20*x2 + 14*x3 >= 15",
        "11*x1 + 14*x3 >= 24",
        "11*x1 + 20*x2 + 14*x3 >= 24",
        "8*x1 + 2*x2 >= 21",
        "8*x1 + 20*x3 >= 23",
        "2*x2 + 20*x3 >= 16",
        "8*x1 + 2*x2 + 20*x3 >= 14",
        "-5*x1^2 + 7*x2^2 >= 0",
        "4*x2 + 6*x3 <= 70",
        "5*x1^2 + 2*x2^2 <= 49",
        "11*x1 + 14*x3 <= 75",
        "2*x2^2 + 20*x3^2 <= 64"
    ]
}
```