## Problem Description and Formulation

The problem is an optimization problem with two variables: 'grams of protein' and 'milligrams of vitamin D'. The objective is to minimize the function $7 \times \text{grams of protein} + 3 \times \text{milligrams of vitamin D}$, subject to several constraints.

### Variables and Resources

- Variables: 
  - $x_0$ = 'grams of protein'
  - $x_1$ = 'milligrams of vitamin D'

- Resources/Attributes:
  - $r_0$: kidney support index
  - $r_1$: cardiovascular support index

### Constraints

1. $\text{kidney support index from } x_0 = 15x_0$
2. $\text{kidney support index from } x_1 = 14x_1$
3. $\text{cardiovascular support index from } x_0 = 5x_0$
4. $\text{cardiovascular support index from } x_1 = 25x_1$

### Mathematical Formulation

- Objective: $\min \ 7x_0 + 3x_1$
- Subject to:
  - $15x_0 + 14x_1 \geq 33$ (kidney support index minimum)
  - $5x_0 + 25x_1 \geq 78$ (cardiovascular support index minimum)
  - $9x_0 - 6x_1 \geq 0$
  - $15x_0 + 14x_1 \leq 75$ (kidney support index upper bound)
  - $5x_0 + 25x_1 \leq 189$ (cardiovascular support index upper bound)
  - $x_0 \in \mathbb{Z}$ (integer constraint for grams of protein)
  - $x_1 \in \mathbb{R}$ (no restriction for milligrams of vitamin D)

## Gurobi Code

```python
import gurobipy as gp

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

# Define variables
x0 = m.addVar(name="grams_of_protein", vtype=gp.GRB.INTEGER)  # Integer variable
x1 = m.addVar(name="milligrams_of_vitamin_D")  # Continuous variable

# Objective function: minimize 7 * x0 + 3 * x1
m.setObjective(7 * x0 + 3 * x1, gp.GRB.MINIMIZE)

# Constraints
m.addConstr(15 * x0 + 14 * x1 >= 33, name="kidney_support_min")
m.addConstr(5 * x0 + 25 * x1 >= 78, name="cardiovascular_support_min")
m.addConstr(9 * x0 - 6 * x1 >= 0, name="protein_vitamin_balance")
m.addConstr(15 * x0 + 14 * x1 <= 75, name="kidney_support_max")
m.addConstr(5 * x0 + 25 * x1 <= 189, name="cardiovascular_support_max")

# Solve the model
m.optimize()

# Print the solution
if m.status == gp.GRB.OPTIMAL:
    print("Optimal solution found.")
    print(f"Grams of protein: {x0.varValue}")
    print(f"Milligrams of vitamin D: {x1.varValue}")
    print(f"Objective: {m.objVal}")
else:
    print("No optimal solution found.")
```