## Problem Description and Formulation

The problem is an optimization problem with the goal of minimizing an objective function subject to several constraints. The variables are:

- $x_0$: milligrams of zinc
- $x_1$: milligrams of vitamin B5
- $x_2$: milligrams of vitamin B7

The objective function to minimize is:

$2.4x_0 + 9.41x_1 + 7.62x_2$

The constraints are:

1. $28x_0 \leq 179$
2. $21x_0 \leq 284$
3. $28x_1 \leq 179$
4. $29x_1 \leq 284$
5. $12x_2 \leq 179$
6. $11x_2 \leq 284$
7. $28x_0 + 12x_2 \geq 21$
8. $28x_1 + 12x_2 \geq 22$
9. $28x_0 + 28x_1 + 12x_2 \geq 22$
10. $29x_1 + 11x_2 \geq 33$
11. $21x_0 + 29x_1 \geq 75$
12. $21x_0 + 11x_2 \geq 35$
13. $21x_0 + 29x_1 + 11x_2 \geq 61$
14. $-3x_0 + 7x_1 \geq 0$
15. $-10x_0 + 6x_2 \geq 0$
16. $28x_1 + 12x_2 \leq 156$
17. $28x_0 + 28x_1 + 12x_2 \leq 138$
18. $21x_0 + 11x_2 \leq 276$
19. $21x_0 + 29x_1 \leq 203$

## Gurobi Code

```python
import gurobi

def optimize():
    # Create a new model
    model = gurobi.Model()

    # Define the variables
    x0 = model.addVar(name="milligrams_of_zinc", lb=0)
    x1 = model.addVar(name="milligrams_of_vitamin_B5", lb=0)
    x2 = model.addVar(name="milligrams_of_vitamin_B7", lb=0)

    # Objective function
    model.setObjective(2.4 * x0 + 9.41 * x1 + 7.62 * x2, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(28 * x0 <= 179, name="kidney_support_zinc")
    model.addConstr(21 * x0 <= 284, name="digestive_support_zinc")
    model.addConstr(28 * x1 <= 179, name="kidney_support_B5")
    model.addConstr(29 * x1 <= 284, name="digestive_support_B5")
    model.addConstr(12 * x2 <= 179, name="kidney_support_B7")
    model.addConstr(11 * x2 <= 284, name="digestive_support_B7")

    model.addConstr(28 * x0 + 12 * x2 >= 21, name="combined_kidney_zinc_B7")
    model.addConstr(28 * x1 + 12 * x2 >= 22, name="combined_kidney_B5_B7")
    model.addConstr(28 * x0 + 28 * x1 + 12 * x2 >= 22, name="combined_kidney_all")

    model.addConstr(29 * x1 + 11 * x2 >= 33, name="combined_digestive_B5_B7")
    model.addConstr(21 * x0 + 29 * x1 >= 75, name="combined_digestive_zinc_B5")
    model.addConstr(21 * x0 + 11 * x2 >= 35, name="combined_digestive_zinc_B7")
    model.addConstr(21 * x0 + 29 * x1 + 11 * x2 >= 61, name="combined_digestive_all")

    model.addConstr(-3 * x0 + 7 * x1 >= 0, name="zinc_B5_constraint")
    model.addConstr(-10 * x0 + 6 * x2 >= 0, name="zinc_B7_constraint")

    model.addConstr(28 * x1 + 12 * x2 <= 156, name="max_kidney_B5_B7")
    model.addConstr(28 * x0 + 28 * x1 + 12 * x2 <= 138, name="max_kidney_all")
    model.addConstr(21 * x0 + 11 * x2 <= 276, name="max_digestive_zinc_B7")
    model.addConstr(21 * x0 + 29 * x1 <= 203, name="max_digestive_zinc_B5")

    # Optimize the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Optimal solution found.")
        print(f"Milligrams of zinc: {x0.varValue}")
        print(f"Milligrams of vitamin B5: {x1.varValue}")
        print(f"Milligrams of vitamin B7: {x2.varValue}")
        print(f"Objective function value: {model.objVal}")
    else:
        print("No optimal solution found.")

optimize()
```