## Step 1: Define the symbolic representation of the problem
The problem involves minimizing an objective function subject to several constraints. The variables are 'grams of protein', 'milligrams of potassium', 'milligrams of vitamin B4', and 'milligrams of vitamin B3', which we can denote as $x_0$, $x_1$, $x_2$, and $x_3$ respectively.

## Step 2: Translate the objective function into symbolic notation
The objective function to minimize is $8.14x_0 + 4.73x_1 + 7.96x_2 + 3.19x_3$.

## 3: List the constraints in symbolic notation
The constraints are:
- $6x_0 \leq 693$
- $5x_0 \leq 670$
- $28x_0 \leq 610$
- $28x_1 \leq 693$
- $4x_1 \leq 670$
- $26x_1 \leq 610$
- $1x_2 \leq 693$
- $9x_2 \leq 670$
- $26x_2 \leq 610$
- $22x_3 \leq 693$
- $8x_3 \leq 670$
- $12x_3 \leq 610$
- $6x_0 + 22x_3 \geq 127$
- $6x_0 + 28x_1 \geq 104$
- $28x_1 + 22x_3 \geq 147$
- $1x_2 + 22x_3 \geq 167$
- $6x_0 + 28x_1 + 22x_3 \geq 111$
- $6x_0 + 28x_1 + 1x_2 + 22x_3 \geq 111$
- $5x_0 + 9x_2 \geq 91$
- $5x_0 + 8x_3 \geq 71$
- $4x_1 + 9x_2 \geq 114$
- $5x_0 + 4x_1 + 9x_2 + 8x_3 \geq 114$
- $28x_0 + 12x_3 \geq 121$
- $28x_0 + 26x_2 \geq 68$
- $26x_2 + 12x_3 \geq 108$
- $28x_0 + 26x_1 \geq 120$
- $26x_1 + 12x_3 \geq 108$
- $28x_0 + 26x_1 + 12x_3 \geq 108$
- $28x_0 + 26x_2 + 12x_3 \geq 108$
- $28x_0 + 26x_1 + 12x_3 \geq 146$
- $28x_0 + 26x_2 + 12x_3 \geq 146$
- $28x_0 + 26x_1 + 26x_2 + 12x_3 \geq 146$
- $1x_2 - 5x_3 \geq 0$
- $1x_2 + 22x_3 \leq 553$
- $28x_1 + 1x_2 \leq 554$
- $6x_0 + 22x_3 \leq 231$
- $6x_0 + 28x_1 \leq 178$
- $6x_0 + 28x_1 + 22x_3 \leq 508$
- $6x_0 + 1x_2 + 22x_3 \leq 304$
- $5x_0 + 4x_1 \leq 411$
- $5x_0 + 8x_3 \leq 539$
- $4x_1 + 9x_2 \leq 357$
- $4x_1 + 8x_3 \leq 445$
- $5x_0 + 9x_2 \leq 266$
- $5x_0 + 4x_1 + 8x_3 \leq 459$
- $5x_0 + 9x_2 + 8x_3 \leq 322$

## 4: Provide the symbolic representation in JSON format
```json
{
    'sym_variables': [
        ('x0', 'grams of protein'),
        ('x1', 'milligrams of potassium'),
        ('x2', 'milligrams of vitamin B4'),
        ('x3', 'milligrams of vitamin B3')
    ],
    'objective_function': '8.14*x0 + 4.73*x1 + 7.96*x2 + 3.19*x3',
    'constraints': [
        '6*x0 <= 693',
        '5*x0 <= 670',
        '28*x0 <= 610',
        '28*x1 <= 693',
        '4*x1 <= 670',
        '26*x1 <= 610',
        '1*x2 <= 693',
        '9*x2 <= 670',
        '26*x2 <= 610',
        '22*x3 <= 693',
        '8*x3 <= 670',
        '12*x3 <= 610',
        '6*x0 + 22*x3 >= 127',
        '6*x0 + 28*x1 >= 104',
        '28*x1 + 22*x3 >= 147',
        '1*x2 + 22*x3 >= 167',
        '6*x0 + 28*x1 + 22*x3 >= 111',
        '6*x0 + 28*x1 + 1*x2 + 22*x3 >= 111',
        '5*x0 + 9*x2 >= 91',
        '5*x0 + 8*x3 >= 71',
        '4*x1 + 9*x2 >= 114',
        '5*x0 + 4*x1 + 9*x2 + 8*x3 >= 114',
        '28*x0 + 12*x3 >= 121',
        '28*x0 + 26*x2 >= 68',
        '26*x2 + 12*x3 >= 108',
        '28*x0 + 26*x1 >= 120',
        '26*x1 + 12*x3 >= 108',
        '28*x0 + 26*x1 + 12*x3 >= 108',
        '28*x0 + 26*x2 + 12*x3 >= 108',
        '28*x0 + 26*x1 + 12*x3 >= 146',
        '28*x0 + 26*x2 + 12*x3 >= 146',
        '28*x0 + 26*x1 + 26*x2 + 12*x3 >= 146',
        '1*x2 - 5*x3 >= 0',
        '1*x2 + 22*x3 <= 553',
        '28*x1 + 1*x2 <= 554',
        '6*x0 + 22*x3 <= 231',
        '6*x0 + 28*x1 <= 178',
        '6*x0 + 28*x1 + 22*x3 <= 508',
        '6*x0 + 1*x2 + 22*x3 <= 304',
        '5*x0 + 4*x1 <= 411',
        '5*x0 + 8*x3 <= 539',
        '4*x1 + 9*x2 <= 357',
        '4*x1 + 8*x3 <= 445',
        '5*x0 + 9*x2 <= 266',
        '5*x0 + 4*x1 + 8*x3 <= 459',
        '5*x0 + 9*x2 + 8*x3 <= 322'
    ]
}
```

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

# Define the model
m = gp.Model()

# Define the variables
x0 = m.addVar(name="x0", lb=0)  # grams of protein
x1 = m.addVar(name="x1", lb=0)  # milligrams of potassium
x2 = m.addVar(name="x2", lb=0)  # milligrams of vitamin B4
x3 = m.addVar(name="x3", lb=0)  # milligrams of vitamin B3

# Objective function
m.setObjective(8.14 * x0 + 4.73 * x1 + 7.96 * x2 + 3.19 * x3, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(6 * x0 <= 693)
m.addConstr(5 * x0 <= 670)
m.addConstr(28 * x0 <= 610)
m.addConstr(28 * x1 <= 693)
m.addConstr(4 * x1 <= 670)
m.addConstr(26 * x1 <= 610)
m.addConstr(x2 <= 693)
m.addConstr(9 * x2 <= 670)
m.addConstr(26 * x2 <= 610)
m.addConstr(22 * x3 <= 693)
m.addConstr(8 * x3 <= 670)
m.addConstr(12 * x3 <= 610)
m.addConstr(6 * x0 + 22 * x3 >= 127)
m.addConstr(6 * x0 + 28 * x1 >= 104)
m.addConstr(28 * x1 + 22 * x3 >= 147)
m.addConstr(x2 + 22 * x3 >= 167)
m.addConstr(6 * x0 + 28 * x1 + 22 * x3 >= 111)
m.addConstr(6 * x0 + 28 * x1 + x2 + 22 * x3 >= 111)
m.addConstr(5 * x0 + 9 * x2 >= 91)
m.addConstr(5 * x0 + 8 * x3 >= 71)
m.addConstr(4 * x1 + 9 * x2 >= 114)
m.addConstr(5 * x0 + 4 * x1 + 9 * x2 + 8 * x3 >= 114)
m.addConstr(28 * x0 + 12 * x3 >= 121)
m.addConstr(28 * x0 + 26 * x2 >= 68)
m.addConstr(26 * x2 + 12 * x3 >= 108)
m.addConstr(28 * x0 + 26 * x1 >= 120)
m.addConstr(26 * x1 + 12 * x3 >= 108)
m.addConstr(28 * x0 + 26 * x1 + 12 * x3 >= 108)
m.addConstr(28 * x0 + 26 * x2 + 12 * x3 >= 108)
m.addConstr(28 * x0 + 26 * x1 + 12 * x3 >= 146)
m.addConstr(28 * x0 + 26 * x2 + 12 * x3 >= 146)
m.addConstr(28 * x0 + 26 * x1 + 26 * x2 + 12 * x3 >= 146)
m.addConstr(x2 - 5 * x3 >= 0)
m.addConstr(x2 + 22 * x3 <= 553)
m.addConstr(28 * x1 + x2 <= 554)
m.addConstr(6 * x0 + 22 * x3 <= 231)
m.addConstr(6 * x0 + 28 * x1 <= 178)
m.addConstr(6 * x0 + 28 * x1 + 22 * x3 <= 508)
m.addConstr(6 * x0 + x2 + 22 * x3 <= 304)
m.addConstr(5 * x0 + 4 * x1 <= 411)
m.addConstr(5 * x0 + 8 * x3 <= 539)
m.addConstr(4 * x1 + 9 * x2 <= 357)
m.addConstr(4 * x1 + 8 * x3 <= 445)
m.addConstr(5 * x0 + 9 * x2 <= 266)
m.addConstr(5 * x0 + 4 * x1 + 8 * x3 <= 459)
m.addConstr(5 * x0 + 9 * x2 + 8 * x3 <= 322)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Objective: ", m.objVal)
    print("x0: ", x0.varValue)
    print("x1: ", x1.varValue)
    print("x2: ", x2.varValue)
    print("x3: ", x3.varValue)
else:
    print("The model is infeasible")
```