## Problem Description and Symbolic Representation

The problem requires finding the optimal number of blue and red jelly pouches a patient should purchase to minimize costs while meeting mineral requirements.

### Symbolic Representation

Let's define the symbolic variables:
- $x_1$ represents the number of blue jelly pouches
- $x_2$ represents the number of red jelly pouches

The objective function to minimize is the total cost: $5x_1 + 7x_2$

The constraints based on the mineral requirements are:
- Calcium: $2x_1 + 3x_2 \geq 30$
- Potassium: $x_1 + 2x_2 \geq 25$
- Sodium: $3x_1 + x_2 \geq 30$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'blue jelly pouches'), ('x2', 'red jelly pouches')],
    'objective_function': '5*x1 + 7*x2',
    'constraints': [
        '2*x1 + 3*x2 >= 30',
        'x1 + 2*x2 >= 25',
        '3*x1 + x2 >= 30',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

def solve_jelly_pouch_problem():
    # Create a new model
    model = gp.Model("jelly_pouch_problem")

    # Define variables
    x1 = model.addVar(name="blue_jelly_pouches", lb=0, vtype=gp.GRB.INTEGER)
    x2 = model.addVar(name="red_jelly_pouches", lb=0, vtype=gp.GRB.INTEGER)

    # Define objective function
    model.setObjective(5 * x1 + 7 * x2, gp.GRB.MINIMIZE)

    # Define constraints
    model.addConstr(2 * x1 + 3 * x2 >= 30, name="calcium_requirement")
    model.addConstr(x1 + 2 * x2 >= 25, name="potassium_requirement")
    model.addConstr(3 * x1 + x2 >= 30, name="sodium_requirement")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gp.GRB.OPTIMAL:
        print(f"Optimal solution: blue jelly pouches = {x1.varValue}, red jelly pouches = {x2.varValue}")
        print(f"Minimum cost: ${model.objVal:.2f}")
    else:
        print("No optimal solution found.")

solve_jelly_pouch_problem()
```