## Problem Description and Formulation

The patient needs to meet daily calcium and vitamin D requirements by consuming milk and cheese. The goal is to minimize the cost of these items while meeting or exceeding the nutritional requirements.

### Variables
- Let \(M\) be the number of servings of milk.
- Let \(C\) be the number of servings of cheese.

### Objective Function
The objective is to minimize the total cost, given by \(2M + 4C\), as a serving of milk costs $2 and a serving of cheese costs $4.

### Constraints
1. Calcium requirement: \(10M + 8C \geq 100\)
2. Vitamin D requirement: \(5M + 6C \geq 80\)
3. Non-negativity constraints: \(M \geq 0, C \geq 0\)

## Gurobi Code

```python
import gurobi

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

    # Define variables
    M = model.addVar(lb=0, name="Milk")
    C = model.addVar(lb=0, name="Cheese")

    # Objective function: minimize cost
    model.setObjective(2 * M + 4 * C, gurobi.GRB.MINIMIZE)

    # Constraints
    model.addConstr(10 * M + 8 * C >= 100, name="Calcium_Requirement")
    model.addConstr(5 * M + 6 * C >= 80, name="VitaminD_Requirement")

    # Optimize
    model.optimize()

    # Print solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal servings of milk: {M.varValue}")
        print(f"Optimal servings of cheese: {C.varValue}")
        print(f"Optimal cost: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

if __name__ == "__main__":
    solve_patient_diet()
```