## Step 1: Define the optimization problem
The goal is to maximize the objective function: $5.81x_0 + 1.67x_1 + 7.59x_2 + 7.7x_3$, where $x_0$ represents milligrams of vitamin B3, $x_1$ represents milligrams of iron, $x_2$ represents milligrams of vitamin D, and $x_3$ represents milligrams of calcium.

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

- $16x_0 \leq 522$
- $33x_0 \leq 300$
- $27x_0 \leq 175$
- $34x_1 \leq 522$
- $20x_1 \leq 300$
- $7x_1 \leq 175$
- $9x_2 \leq 522$
- $34x_2 \leq 300$
- $34x_2 \leq 175$
- $18x_3 \leq 522$
- $30x_3 \leq 300$
- $4x_3 \leq 175$
- $16x_0 + 9x_2 \geq 50$
- $16x_0 + 18x_3 \geq 49$
- $16x_0 + 34x_1 \geq 72$
- $34x_1 + 9x_2 \geq 128$
- $16x_0 + 9x_2 + 18x_3 \geq 109$
- $34x_1 + 9x_2 + 18x_3 \geq 109$
- $16x_0 + 9x_2 + 18x_3 \geq 79$
- $34x_1 + 9x_2 + 18x_3 \geq 79$
- $33x_0 + 20x_1 + 30x_3 \geq 56$
- $33x_0 + 20x_1 + 34x_2 \geq 56$
- $20x_1 + 34x_2 + 30x_3 \geq 56$
- $33x_0 + 20x_1 + 30x_3 \geq 50$
- $33x_0 + 20x_1 + 34x_2 \geq 50$
- $20x_1 + 34x_2 + 30x_3 \geq 50$
- $33x_0 + 20x_1 + 30x_3 \geq 42$
- $33x_0 + 20x_1 + 34x_2 \geq 42$
- $20x_1 + 34x_2 + 30x_3 \geq 42$
- $27x_0 + 34x_2 \geq 20$
- $27x_0 + 7x_1 \geq 39$
- $34x_2 + 4x_3 \geq 15$
- $7x_1 + 4x_3 \geq 42$
- $27x_0 + 34x_2 + 4x_3 \geq 43$
- $16x_0 + 18x_3 \leq 179$
- $16x_0 + 34x_1 \leq 340$
- $16x_0 + 9x_2 \leq 483$
- $34x_1 + 18x_3 \leq 479$
- $9x_2 + 18x_3 \leq 491$
- $16x_0 + 34x_1 + 9x_2 \leq 241$
- $16x_0 + 9x_2 + 18x_3 \leq 295$
- $16x_0 + 34x_1 + 18x_3 \leq 292$
- $16x_0 + 34x_1 + 9x_2 + 18x_3 \leq 292$
- $20x_1 + 34x_2 \leq 154$
- $34x_2 + 30x_3 \leq 265$
- $33x_0 + 30x_3 \leq 159$
- $33x_0 + 34x_2 \leq 209$
- $33x_0 + 20x_1 + 34x_2 + 30x_3 \leq 209$
- $7x_1 + 34x_2 \leq 88$
- $27x_0 + 7x_1 \leq 65$
- $27x_0 + 34x_2 \leq 73$
- $34x_2 + 4x_3 \leq 95$
- $27x_0 + 7x_1 + 34x_2 + 4x_3 \leq 95$

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

```python
import gurobi as gp

# Create a new model
m = gp.Model("optimization_problem")

# Define variables
x0 = m.addVar(name="milligrams of vitamin B3", lb=-gp.GRB.INFINITY)
x1 = m.addVar(name="milligrams of iron", lb=-gp.GRB.INFINITY)
x2 = m.addVar(name="milligrams of vitamin D", lb=-gp.GRB.INFINITY)
x3 = m.addVar(name="milligrams of calcium", lb=-gp.GRB.INFINITY)

# Objective function
m.setObjective(5.81*x0 + 1.67*x1 + 7.59*x2 + 7.7*x3, gp.GRB.MAXIMIZE)

# Constraints
m.addConstr(16*x0 <= 522)
m.addConstr(33*x0 <= 300)
m.addConstr(27*x0 <= 175)
m.addConstr(34*x1 <= 522)
m.addConstr(20*x1 <= 300)
m.addConstr(7*x1 <= 175)
m.addConstr(9*x2 <= 522)
m.addConstr(34*x2 <= 300)
m.addConstr(34*x2 <= 175)
m.addConstr(18*x3 <= 522)
m.addConstr(30*x3 <= 300)
m.addConstr(4*x3 <= 175)

m.addConstr(16*x0 + 9*x2 >= 50)
m.addConstr(16*x0 + 18*x3 >= 49)
m.addConstr(16*x0 + 34*x1 >= 72)
m.addConstr(34*x1 + 9*x2 >= 128)
m.addConstr(16*x0 + 9*x2 + 18*x3 >= 109)
m.addConstr(34*x1 + 9*x2 + 18*x3 >= 109)
m.addConstr(16*x0 + 9*x2 + 18*x3 >= 79)
m.addConstr(34*x1 + 9*x2 + 18*x3 >= 79)

m.addConstr(33*x0 + 20*x1 + 30*x3 >= 56)
m.addConstr(33*x0 + 20*x1 + 34*x2 >= 56)
m.addConstr(20*x1 + 34*x2 + 30*x3 >= 56)
m.addConstr(33*x0 + 20*x1 + 30*x3 >= 50)
m.addConstr(33*x0 + 20*x1 + 34*x2 >= 50)
m.addConstr(20*x1 + 34*x2 + 30*x3 >= 50)
m.addConstr(33*x0 + 20*x1 + 30*x3 >= 42)
m.addConstr(33*x0 + 20*x1 + 34*x2 >= 42)
m.addConstr(20*x1 + 34*x2 + 30*x3 >= 42)

m.addConstr(27*x0 + 34*x2 >= 20)
m.addConstr(27*x0 + 7*x1 >= 39)
m.addConstr(34*x2 + 4*x3 >= 15)
m.addConstr(7*x1 + 4*x3 >= 42)
m.addConstr(27*x0 + 34*x2 + 4*x3 >= 43)

m.addConstr(16*x0 + 18*x3 <= 179)
m.addConstr(16*x0 + 34*x1 <= 340)
m.addConstr(16*x0 + 9*x2 <= 483)
m.addConstr(34*x1 + 18*x3 <= 479)
m.addConstr(9*x2 + 18*x3 <= 491)
m.addConstr(16*x0 + 34*x1 + 9*x2 <= 241)
m.addConstr(16*x0 + 9*x2 + 18*x3 <= 295)
m.addConstr(16*x0 + 34*x1 + 18*x3 <= 292)
m.addConstr(16*x0 + 34*x1 + 9*x2 + 18*x3 <= 292)

m.addConstr(20*x1 + 34*x2 <= 154)
m.addConstr(34*x2 + 30*x3 <= 265)
m.addConstr(33*x0 + 30*x3 <= 159)
m.addConstr(33*x0 + 34*x2 <= 209)
m.addConstr(33*x0 + 20*x1 + 34*x2 + 30*x3 <= 209)

m.addConstr(7*x1 + 34*x2 <= 88)
m.addConstr(27*x0 + 7*x1 <= 65)
m.addConstr(27*x0 + 34*x2 <= 73)
m.addConstr(34*x2 + 4*x3 <= 95)
m.addConstr(27*x0 + 7*x1 + 34*x2 + 4*x3 <= 95)

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print("Milligrams of vitamin B3: ", x0.varValue)
    print("Milligrams of iron: ", x1.varValue)
    print("Milligrams of vitamin D: ", x2.varValue)
    print("Milligrams of calcium: ", x3.varValue)
    print("Objective function value: ", m.objVal)
else:
    print("No optimal solution found.")
```