## Step 1: Define the symbolic representation of the variables
The variables are defined as follows: 
- $x_0$ represents 'milligrams of vitamin B6'
- $x_1$ represents 'milligrams of vitamin B7'
- $x_2$ represents 'grams of protein'
- $x_3$ represents 'milligrams of zinc'

## Step 2: Formulate the objective function
The objective function to minimize is $6.77x_0 + 6.7x_1 + 8.2x_2 + 9.77x_3$.

## 3: List all the constraints
The constraints are:
- $16.76x_0 \leq 374$
- $17.28x_0 \leq 321$
- $13.75x_1 \leq 374$
- $1.28x_1 \leq 321$
- $3.76x_2 \leq 374$
- $10.19x_2 \leq 321$
- $12.02x_3 \leq 374$
- $2.48x_3 \leq 321$
- $16.76x_0 + 13.75x_1 \geq 83$
- $16.76x_0 + 3.76x_2 \geq 79$
- $13.75x_1 + 3.76x_2 \geq 61$
- $16.76x_0 + 12.02x_3 \geq 80$
- $13.75x_1 + 12.02x_3 \geq 42$
- $3.76x_2 + 12.02x_3 \geq 36$
- $16.76x_0 + 13.75x_1 + 3.76x_2 \geq 46$
- $16.76x_0 + 13.75x_1 + 12.02x_3 \geq 46$
- $16.76x_0 + 3.76x_2 + 12.02x_3 \geq 46$
- $16.76x_0 + 13.75x_1 + 3.76x_2 \geq 81$
- $16.76x_0 + 13.75x_1 + 12.02x_3 \geq 81$
- $16.76x_0 + 3.76x_2 + 12.02x_3 \geq 81$
- $16.76x_0 + 13.75x_1 + 3.76x_2 \geq 62$
- $16.76x_0 + 13.75x_1 + 12.02x_3 \geq 62$
- $16.76x_0 + 3.76x_2 + 12.02x_3 \geq 62$
- $16.76x_0 + 13.75x_1 + 3.76x_2 + 12.02x_3 \geq 62$
- $1.28x_1 + 10.19x_2 \geq 43$
- $17.28x_0 + 10.19x_2 + 2.48x_3 \geq 70$
- $17.28x_0 + 1.28x_1 + 10.19x_2 + 2.48x_3 \geq 70$
- $5x_1 - 8x_2 \geq 0$
- $-3x_2 + 4x_3 \geq 0$
- $13.75x_1 + 3.76x_2 + 12.02x_3 \leq 357$
- $16.76x_0 + 13.75x_1 + 3.76x_2 \leq 219$
- $17.28x_0 + 2.48x_3 \leq 113$
- $17.28x_0 + 10.19x_2 \leq 311$
- $1.28x_1 + 10.19x_2 \leq 310$
- $10.19x_2 + 2.48x_3 \leq 246$
- $17.28x_0 + 1.28x_1 \leq 302$
- $x_0$ is an integer
- $x_2$ is an integer
- $x_3$ is an integer

## 4: Write the Gurobi code
```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="x0", vtype=gurobi.GRB.INTEGER)  # milligrams of vitamin B6
    x1 = model.addVar(name="x1")  # milligrams of vitamin B7
    x2 = model.addVar(name="x2", vtype=gurobi.GRB.INTEGER)  # grams of protein
    x3 = model.addVar(name="x3", vtype=gurobi.GRB.INTEGER)  # milligrams of zinc

    # Objective function
    model.setObjective(6.77 * x0 + 6.7 * x1 + 8.2 * x2 + 9.77 * x3, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(16.76 * x0 <= 374)
    model.addConstr(17.28 * x0 <= 321)
    model.addConstr(13.75 * x1 <= 374)
    model.addConstr(1.28 * x1 <= 321)
    model.addConstr(3.76 * x2 <= 374)
    model.addConstr(10.19 * x2 <= 321)
    model.addConstr(12.02 * x3 <= 374)
    model.addConstr(2.48 * x3 <= 321)

    model.addConstr(16.76 * x0 + 13.75 * x1 >= 83)
    model.addConstr(16.76 * x0 + 3.76 * x2 >= 79)
    model.addConstr(13.75 * x1 + 3.76 * x2 >= 61)
    model.addConstr(16.76 * x0 + 12.02 * x3 >= 80)
    model.addConstr(13.75 * x1 + 12.02 * x3 >= 42)
    model.addConstr(3.76 * x2 + 12.02 * x3 >= 36)

    model.addConstr(16.76 * x0 + 13.75 * x1 + 3.76 * x2 >= 46)
    model.addConstr(16.76 * x0 + 13.75 * x1 + 12.02 * x3 >= 46)
    model.addConstr(16.76 * x0 + 3.76 * x2 + 12.02 * x3 >= 46)

    model.addConstr(16.76 * x0 + 13.75 * x1 + 3.76 * x2 >= 81)
    model.addConstr(16.76 * x0 + 13.75 * x1 + 12.02 * x3 >= 81)
    model.addConstr(16.76 * x0 + 3.76 * x2 + 12.02 * x3 >= 81)

    model.addConstr(16.76 * x0 + 13.75 * x1 + 3.76 * x2 >= 62)
    model.addConstr(16.76 * x0 + 13.75 * x1 + 12.02 * x3 >= 62)
    model.addConstr(16.76 * x0 + 3.76 * x2 + 12.02 * x3 >= 62)
    model.addConstr(16.76 * x0 + 13.75 * x1 + 3.76 * x2 + 12.02 * x3 >= 62)

    model.addConstr(1.28 * x1 + 10.19 * x2 >= 43)
    model.addConstr(17.28 * x0 + 10.19 * x2 + 2.48 * x3 >= 70)
    model.addConstr(17.28 * x0 + 1.28 * x1 + 10.19 * x2 + 2.48 * x3 >= 70)

    model.addConstr(5 * x1 - 8 * x2 >= 0)
    model.addConstr(-3 * x2 + 4 * x3 >= 0)

    model.addConstr(13.75 * x1 + 3.76 * x2 + 12.02 * x3 <= 357)
    model.addConstr(16.76 * x0 + 13.75 * x1 + 3.76 * x2 <= 219)
    model.addConstr(17.28 * x0 + 2.48 * x3 <= 113)
    model.addConstr(17.28 * x0 + 10.19 * x2 <= 311)
    model.addConstr(1.28 * x1 + 10.19 * x2 <= 310)
    model.addConstr(10.19 * x2 + 2.48 * x3 <= 246)
    model.addConstr(17.28 * x0 + 1.28 * x1 <= 302)

    model.optimize()

    if model.status == gurobi.GRB.Status.OPTIMAL:
        print("Optimal solution found.")
        print("milligrams of vitamin B6: ", x0.varValue)
        print("milligrams of vitamin B7: ", x1.varValue)
        print("grams of protein: ", x2.varValue)
        print("milligrams of zinc: ", x3.varValue)
    else:
        print("No optimal solution found.")

optimize()
```

## 5: Symbolic representation
```json
{
    'sym_variables': [
        ('x0', 'milligrams of vitamin B6'), 
        ('x1', 'milligrams of vitamin B7'), 
        ('x2', 'grams of protein'), 
        ('x3', 'milligrams of zinc')
    ], 
    'objective_function': '6.77*x0 + 6.7*x1 + 8.2*x2 + 9.77*x3', 
    'constraints': [
        '16.76*x0 <= 374',
        '17.28*x0 <= 321',
        '13.75*x1 <= 374',
        '1.28*x1 <= 321',
        '3.76*x2 <= 374',
        '10.19*x2 <= 321',
        '12.02*x3 <= 374',
        '2.48*x3 <= 321',
        '16.76*x0 + 13.75*x1 >= 83',
        '16.76*x0 + 3.76*x2 >= 79',
        '13.75*x1 + 3.76*x2 >= 61',
        '16.76*x0 + 12.02*x3 >= 80',
        '13.75*x1 + 12.02*x3 >= 42',
        '3.76*x2 + 12.02*x3 >= 36',
        '16.76*x0 + 13.75*x1 + 3.76*x2 >= 46',
        '16.76*x0 + 13.75*x1 + 12.02*x3 >= 46',
        '16.76*x0 + 3.76*x2 + 12.02*x3 >= 46',
        '16.76*x0 + 13.75*x1 + 3.76*x2 >= 81',
        '16.76*x0 + 13.75*x1 + 12.02*x3 >= 81',
        '16.76*x0 + 3.76*x2 + 12.02*x3 >= 81',
        '16.76*x0 + 13.75*x1 + 3.76*x2 >= 62',
        '16.76*x0 + 13.75*x1 + 12.02*x3 >= 62',
        '16.76*x0 + 3.76*x2 + 12.02*x3 >= 62',
        '16.76*x0 + 13.75*x1 + 3.76*x2 + 12.02*x3 >= 62',
        '1.28*x1 + 10.19*x2 >= 43',
        '17.28*x0 + 10.19*x2 + 2.48*x3 >= 70',
        '17.28*x0 + 1.28*x1 + 10.19*x2 + 2.48*x3 >= 70',
        '5*x1 - 8*x2 >= 0',
        '-3*x2 + 4*x3 >= 0',
        '13.75*x1 + 3.76*x2 + 12.02*x3 <= 357',
        '16.76*x0 + 13.75*x1 + 3.76*x2 <= 219',
        '17.28*x0 + 2.48*x3 <= 113',
        '17.28*x0 + 10.19*x2 <= 311',
        '1.28*x1 + 10.19*x2 <= 310',
        '10.19*x2 + 2.48*x3 <= 246',
        '17.28*x0 + 1.28*x1 <= 302'
    ]
}
```