## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The patient needs to meet certain mineral requirements by purchasing blue and red jelly pouches. Each type of jelly pouch contains different amounts of calcium, potassium, and sodium. The goal is to minimize the cost while meeting the mineral requirements.

Let's define the variables:
- \(B\): the number of blue jelly pouches to purchase
- \(R\): the number of red jelly pouches to purchase

The objective function to minimize is the total cost:
\[ \text{Minimize:} \quad 5B + 7R \]

Subject to the constraints:
- Calcium: \(2B + 3R \geq 30\)
- Potassium: \(B + 2R \geq 25\)
- Sodium: \(3B + R \geq 30\)
- Non-negativity: \(B \geq 0, R \geq 0\)

## Gurobi Code

```python
import gurobipy as gp

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

# Define the variables
B = model.addVar(name="Blue", lb=0, vtype=gp.GRB.INTEGER)  # Number of blue jelly pouches
R = model.addVar(name="Red", lb=0, vtype=gp.GRB.INTEGER)   # Number of red jelly pouches

# Define the objective function
model.setObjective(5*B + 7*R, gp.GRB.MINIMIZE)

# Add constraints
model.addConstr(2*B + 3*R >= 30, name="Calcium")      # Calcium requirement
model.addConstr(B + 2*R >= 25, name="Potassium")     # Potassium requirement
model.addConstr(3*B + R >= 30, name="Sodium")        # Sodium requirement

# Solve the model
model.optimize()

# Check if the model is optimized
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution: B = {B.varValue}, R = {R.varValue}")
    print(f"Minimum cost: ${5*B.varValue + 7*R.varValue}")
else:
    print("The model is infeasible.")
```