## Step 1: Define the optimization problem
The goal is to minimize the objective function: $8.14x_0 + 4.73x_1 + 7.96x_2 + 3.19x_3$, where $x_0$ represents grams of protein, $x_1$ represents milligrams of potassium, $x_2$ represents milligrams of vitamin B4, and $x_3$ represents milligrams of vitamin B3.

## Step 2: List all constraints
The constraints are as follows:
- $6x_0 \leq 693$
- $5x_0 \leq 670$
- $28x_0 \leq 610$
- $28x_1 \leq 693$
- $4x_1 \leq 670$
- $26x_1 \leq 610$
- $1x_2 \leq 693$
- $9x_2 \leq 670$
- $26x_2 \leq 610$
- $22x_3 \leq 693$
- $8x_3 \leq 670$
- $12x_3 \leq 610$
- $6x_0 + 22x_3 \geq 127$
- $6x_0 + 28x_1 \geq 104$
- $28x_1 + 22x_3 \geq 147$
- $1x_2 + 22x_3 \geq 167$
- $6x_0 + 28x_1 + 22x_3 \geq 111$
- $6x_0 + 28x_1 + 1x_2 + 22x_3 \geq 111$
- $5x_0 + 9x_2 \geq 91$
- $5x_0 + 8x_3 \geq 71$
- $4x_1 + 9x_2 \geq 114$
- $5x_0 + 4x_1 + 9x_2 + 8x_3 \geq 114$
- $28x_0 + 12x_3 \geq 121$
- $28x_0 + 26x_2 \geq 68$
- $26x_2 + 12x_3 \geq 108$
- $28x_0 + 26x_1 \geq 120$
- $26x_1 + 12x_3 \geq 108$
- $28x_0 + 26x_1 + 12x_3 \geq 108$
- $28x_0 + 26x_2 + 12x_3 \geq 108$
- $28x_0 + 26x_1 + 12x_3 \geq 146$
- $28x_0 + 26x_2 + 12x_3 \geq 146$
- $28x_0 + 26x_1 + 26x_2 + 12x_3 \geq 146$
- $1x_2 - 5x_3 \geq 0$
- $1x_2 + 22x_3 \leq 553$
- $28x_1 + 1x_2 \leq 554$
- $6x_0 + 22x_3 \leq 231$
- $6x_0 + 28x_1 \leq 178$
- $6x_0 + 28x_1 + 22x_3 \leq 508$
- $6x_0 + 1x_2 + 22x_3 \leq 304$
- $5x_0 + 4x_1 \leq 411$
- $5x_0 + 8x_3 \leq 539$
- $4x_1 + 9x_2 \leq 357$
- $4x_1 + 8x_3 \leq 445$
- $5x_0 + 9x_2 \leq 266$
- $5x_0 + 4x_1 + 8x_3 \leq 459$
- $5x_0 + 9x_2 + 8x_3 \leq 322$

## Step 3: Implement the optimization problem using Gurobi
```python
import gurobi

def optimize():
    model = gurobi.Model()
    
    # Define variables
    x0 = model.addVar(name="grams_of_protein", lb=0)
    x1 = model.addVar(name="milligrams_of_potassium", lb=0)
    x2 = model.addVar(name="milligrams_of_vitamin_B4", lb=0)
    x3 = model.addVar(name="milligrams_of_vitamin_B3", lb=0)

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

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

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objval)
        print("Grams of protein: ", x0.varValue)
        print("Milligrams of potassium: ", x1.varValue)
        print("Milligrams of vitamin B4: ", x2.varValue)
        print("Milligrams of vitamin B3: ", x3.varValue)
    else:
        print("The model is infeasible")

optimize()
```