## Step 1: Define the optimization problem
The problem is to maximize the objective function: $5.19x_0 + 8.36x_1 + 4.74x_2 + 3.83x_3$, where $x_0$ represents milligrams of vitamin A, $x_1$ represents grams of fat, $x_2$ represents milligrams of vitamin B6, and $x_3$ represents milligrams of vitamin B5.

## Step 2: List all the constraints
The constraints are as follows:

- $12x_0 \leq 75$
- $10x_0 \leq 221$
- $2x_0 \leq 166$
- $12x_1 \leq 75$
- $9x_1 \leq 221$
- $8x_1 \leq 166$
- $13x_2 \leq 75$
- $9x_2 \leq 221$
- $4x_2 \leq 166$
- $4x_3 \leq 75$
- $14x_3 \leq 221$
- $11x_3 \leq 166$
- $12x_0 + 4x_3 \geq 13$
- $12x_0 + 12x_1 + 4x_3 \geq 15$
- $12x_1 + 13x_2 + 4x_3 \geq 15$
- $12x_0 + 12x_1 + 4x_3 \geq 11$
- $12x_1 + 13x_2 + 4x_3 \geq 11$
- $10x_0 + 9x_2 \geq 28$
- $10x_0 + 14x_3 \geq 33$
- $10x_0 + 9x_2 + 14x_3 \geq 44$
- $9x_1 + 9x_2 + 14x_3 \geq 44$
- $10x_0 + 9x_2 + 14x_3 \geq 35$
- $9x_1 + 9x_2 + 14x_3 \geq 35$
- $4x_2 + 11x_3 \geq 28$
- $2x_0 + 11x_3 \geq 30$
- $2x_0 + 8x_1 \geq 26$
- $8x_1 + 4x_2 \geq 30$
- $8x_1 + 4x_2 + 11x_3 \geq 38$
- $12x_0 + 12x_1 \leq 63$
- $12x_1 + 13x_2 \leq 59$
- $12x_0 + 12x_1 + 13x_2 \leq 62$
- $12x_0 + 12x_1 + 4x_3 \leq 57$
- $12x_1 + 13x_2 + 4x_3 \leq 45$
- $12x_0 + 12x_1 + 13x_2 + 4x_3 \leq 45$
- $10x_0 + 14x_3 \leq 193$
- $10x_0 + 9x_2 \leq 183$
- $10x_0 + 9x_1 \leq 162$
- $9x_1 + 9x_2 \leq 118$
- $10x_0 + 9x_2 + 14x_3 \leq 196$
- $10x_0 + 9x_1 + 9x_2 + 14x_3 \leq 196$
- $2x_0 + 11x_3 \leq 65$
- $8x_1 + 4x_2 \leq 58$
- $2x_0 + 8x_1 \leq 77$
- $2x_0 + 8x_1 + 4x_2 + 11x_3 \leq 77$

## Step 3: Implement the optimization problem using Gurobi
We will use the Gurobi library in Python to solve this optimization problem.

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(lb=0, name="milligrams of vitamin A")
    x1 = model.addVar(lb=0, name="grams of fat")
    x2 = model.addVar(lb=0, name="milligrams of vitamin B6")
    x3 = model.addVar(lb=0, name="milligrams of vitamin B5")

    # Objective function
    model.setObjective(5.19*x0 + 8.36*x1 + 4.74*x2 + 3.83*x3, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(12*x0 <= 75)
    model.addConstr(10*x0 <= 221)
    model.addConstr(2*x0 <= 166)
    model.addConstr(12*x1 <= 75)
    model.addConstr(9*x1 <= 221)
    model.addConstr(8*x1 <= 166)
    model.addConstr(13*x2 <= 75)
    model.addConstr(9*x2 <= 221)
    model.addConstr(4*x2 <= 166)
    model.addConstr(4*x3 <= 75)
    model.addConstr(14*x3 <= 221)
    model.addConstr(11*x3 <= 166)

    model.addConstr(12*x0 + 4*x3 >= 13)
    model.addConstr(12*x0 + 12*x1 + 4*x3 >= 15)
    model.addConstr(12*x1 + 13*x2 + 4*x3 >= 15)
    model.addConstr(12*x0 + 12*x1 + 4*x3 >= 11)
    model.addConstr(12*x1 + 13*x2 + 4*x3 >= 11)

    model.addConstr(10*x0 + 9*x2 >= 28)
    model.addConstr(10*x0 + 14*x3 >= 33)
    model.addConstr(10*x0 + 9*x2 + 14*x3 >= 44)
    model.addConstr(9*x1 + 9*x2 + 14*x3 >= 44)
    model.addConstr(10*x0 + 9*x2 + 14*x3 >= 35)
    model.addConstr(9*x1 + 9*x2 + 14*x3 >= 35)

    model.addConstr(4*x2 + 11*x3 >= 28)
    model.addConstr(2*x0 + 11*x3 >= 30)
    model.addConstr(2*x0 + 8*x1 >= 26)
    model.addConstr(8*x1 + 4*x2 >= 30)
    model.addConstr(8*x1 + 4*x2 + 11*x3 >= 38)

    model.addConstr(12*x0 + 12*x1 <= 63)
    model.addConstr(12*x1 + 13*x2 <= 59)
    model.addConstr(12*x0 + 12*x1 + 13*x2 <= 62)
    model.addConstr(12*x0 + 12*x1 + 4*x3 <= 57)
    model.addConstr(12*x1 + 13*x2 + 4*x3 <= 45)
    model.addConstr(12*x0 + 12*x1 + 13*x2 + 4*x3 <= 45)

    model.addConstr(10*x0 + 14*x3 <= 193)
    model.addConstr(10*x0 + 9*x2 <= 183)
    model.addConstr(10*x0 + 9*x1 <= 162)
    model.addConstr(9*x1 + 9*x2 <= 118)
    model.addConstr(10*x0 + 9*x2 + 14*x3 <= 196)
    model.addConstr(10*x0 + 9*x1 + 9*x2 + 14*x3 <= 196)

    model.addConstr(2*x0 + 11*x3 <= 65)
    model.addConstr(8*x1 + 4*x2 <= 58)
    model.addConstr(2*x0 + 8*x1 <= 77)
    model.addConstr(2*x0 + 8*x1 + 4*x2 + 11*x3 <= 77)

    model.optimize()

    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print("Milligrams of vitamin A: ", x0.varValue)
        print("Grams of fat: ", x1.varValue)
        print("Milligrams of vitamin B6: ", x2.varValue)
        print("Milligrams of vitamin B5: ", x3.varValue)
        print("Objective function value: ", model.objVal)
    else:
        print("No optimal solution found.")

optimize()
```