## Problem Description and Formulation

The problem is an optimization problem where we need to maximize a given objective function subject to several constraints. The objective function to maximize is:

\[ 5.81 \times \text{milligrams of vitamin B5} + 4.93 \times \text{milligrams of zinc} + 5.73 \times \text{milligrams of vitamin B7} + 8.21 \times \text{milligrams of vitamin B4} + 8.07 \times \text{milligrams of calcium} \]

The constraints are:

1. The energy stability index for milligrams of vitamin B5 is 5.
2. The energy stability index for milligrams of zinc is 20.
3. The energy stability index for milligrams of vitamin B7 is 31.
4. The energy stability index for milligrams of vitamin B4 is 14.
5. The energy stability index for milligrams of calcium is 31.
6. \( 5x_0 + 20x_1 + 31x_2 \geq 69 \)
7. \( 5x_0 + 20x_1 + 14x_3 \geq 69 \)
8. \( 5x_0 + 20x_1 + 31x_2 \geq 80 \)
9. \( 5x_0 + 20x_1 + 14x_3 \geq 80 \)
10. \( 5x_0 + 31x_4 \leq 486 \)
11. \( 20x_1 + 31x_2 \leq 213 \)
12. \( 5x_0 + 20x_1 + 31x_2 + 14x_3 + 31x_4 \leq 213 \)

Where \( x_0, x_1, x_2, x_3, x_4 \) represent the milligrams of vitamin B5, zinc, vitamin B7, vitamin B4, and calcium respectively.

## Gurobi Code

```python
import gurobi

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

    # Define variables
    x0 = model.addVar(name="vitamin_B5", lb=0)  # milligrams of vitamin B5
    x1 = model.addVar(name="zinc", lb=0)     # milligrams of zinc
    x2 = model.addVar(name="vitamin_B7", lb=0)  # milligrams of vitamin B7
    x3 = model.addVar(name="vitamin_B4", lb=0)  # milligrams of vitamin B4
    x4 = model.addVar(name="calcium", lb=0)    # milligrams of calcium

    # Objective function
    model.setObjective(5.81*x0 + 4.93*x1 + 5.73*x2 + 8.21*x3 + 8.07*x4, gurobi.GRB.MAXIMIZE)

    # Constraints
    model.addConstr(5*x0 + 20*x1 + 31*x2 >= 69)
    model.addConstr(5*x0 + 20*x1 + 14*x3 >= 69)
    model.addConstr(5*x0 + 20*x1 + 31*x2 >= 80)
    model.addConstr(5*x0 + 20*x1 + 14*x3 >= 80)
    model.addConstr(5*x0 + 31*x4 <= 486)
    model.addConstr(20*x1 + 31*x2 <= 213)
    model.addConstr(5*x0 + 20*x1 + 31*x2 + 14*x3 + 31*x4 <= 213)

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print("Objective: ", model.objVal)
        print("Vitamin B5: ", x0.varValue)
        print("Zinc: ", x1.varValue)
        print("Vitamin B7: ", x2.varValue)
        print("Vitamin B4: ", x3.varValue)
        print("Calcium: ", x4.varValue)
    else:
        print("No optimal solution found")

optimize()
```