## Problem Description and Symbolic Representation

The problem involves a grocery store that wants to maximize profit by selling bulk quantities of two mixtures made from almonds, pecans, and pistachios. The store has limited quantities of each nut: 1000 grams of almonds, 1200 grams of pecans, and 1100 grams of pistachios. Mixture 1 contains 20 grams of almonds, 30 grams of pecans, and 10 grams of pistachios, with a profit of $10 per mixture. Mixture 2 contains 15 grams of almonds, 20 grams of pecans, and 25 grams of pistachios, with a profit of $12 per mixture.

### Symbolic Representation

Let's define the symbolic variables:
- $x_1$ represents the number of Mixture 1 to sell
- $x_2$ represents the number of Mixture 2 to sell

The objective is to maximize profit, which can be represented as:
\[ \text{Maximize:} \quad 10x_1 + 12x_2 \]

The constraints based on the available quantities of nuts are:
- Almonds: $20x_1 + 15x_2 \leq 1000$
- Pecans: $30x_1 + 20x_2 \leq 1200$
- Pistachios: $10x_1 + 25x_2 \leq 1100$
- Non-negativity: $x_1 \geq 0, x_2 \geq 0$

## Symbolic Representation in JSON Format

```json
{
    'sym_variables': [('x1', 'Mixture 1'), ('x2', 'Mixture 2')],
    'objective_function': '10*x1 + 12*x2',
    'constraints': [
        '20*x1 + 15*x2 <= 1000',
        '30*x1 + 20*x2 <= 1200',
        '10*x1 + 25*x2 <= 1100',
        'x1 >= 0',
        'x2 >= 0'
    ]
}
```

## Gurobi Code in Python

```python
import gurobipy as gp

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

# Define the variables
x1 = model.addVar(name="Mixture_1", lb=0, vtype=gp.GRB.CONTINUOUS)
x2 = model.addVar(name="Mixture_2", lb=0, vtype=gp.GRB.CONTINUOUS)

# Define the objective function
model.setObjective(10*x1 + 12*x2, gp.GRB.MAXIMIZE)

# Add constraints
model.addConstr(20*x1 + 15*x2 <= 1000, name="Almonds_Constraint")
model.addConstr(30*x1 + 20*x2 <= 1200, name="Pecans_Constraint")
model.addConstr(10*x1 + 25*x2 <= 1100, name="Pistachios_Constraint")

# Solve the model
model.optimize()

# Print the solution
if model.status == gp.GRB.OPTIMAL:
    print(f"Optimal solution found: Mixture 1 = {x1.varValue}, Mixture 2 = {x2.varValue}")
    print(f"Maximum profit: ${model.objVal:.2f}")
else:
    print("No optimal solution found")
```