## Problem Description and Formulation

The problem is an optimization problem that involves minimizing an objective function subject to several constraints. The objective function to be minimized is \(6 \times \text{fruit salads} + 2 \times \text{cantaloupes}\).

The constraints are as follows:
- Each fruit salad contains 3 grams of fiber, 11 grams of protein, and 1 gram of fat.
- Each cantaloupe contains 15 grams of fiber, 17 grams of protein, and 21 grams of fat.
- The total fiber from fruit salads and cantaloupes must be at least 57 grams.
- The total protein from fruit salads and cantaloupes must be at least 61 grams.
- The total fat from fruit salads and cantaloupes must be at least 77 grams.
- The constraint \(-10 \times \text{fruit salads} + 2 \times \text{cantaloupes} \geq 0\) must be satisfied.
- The total fiber from fruit salads and cantaloupes cannot exceed 285 grams.
- The total protein from fruit salads and cantaloupes cannot exceed 216 grams.
- The total fat from fruit salads and cantaloupes cannot exceed 224 grams.

## Gurobi Code Formulation

```python
import gurobi

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

    # Define the variables
    fruit_salads = model.addVar(name="fruit_salads", lb=0)  # Assuming lb=0, but not explicitly stated
    cantaloupes = model.addVar(name="cantaloupes", lb=0)  # Assuming lb=0, but not explicitly stated

    # Define the objective function
    model.setObjective(6 * fruit_salads + 2 * cantaloupes, gurobi.GRB.MINIMIZE)

    # Define the constraints
    # Fiber constraint: 3*fruit_salads + 15*cantaloupes >= 57
    model.addConstr(3 * fruit_salads + 15 * cantaloupes >= 57, name="fiber_constraint")

    # Protein constraint: 11*fruit_salads + 17*cantaloupes >= 61
    model.addConstr(11 * fruit_salads + 17 * cantaloupes >= 61, name="protein_constraint")

    # Fat constraint: 1*fruit_salads + 21*cantaloupes >= 77
    model.addConstr(1 * fruit_salads + 21 * cantaloupes >= 77, name="fat_constraint")

    # Mixed constraint: -10*fruit_salads + 2*cantaloupes >= 0
    model.addConstr(-10 * fruit_salads + 2 * cantaloupes >= 0, name="mixed_constraint")

    # Upper bounds
    # Fiber upper bound: 3*fruit_salads + 15*cantaloupes <= 285
    model.addConstr(3 * fruit_salads + 15 * cantaloupes <= 285, name="fiber_upper_bound")

    # Protein upper bound: 11*fruit_salads + 17*cantaloupes <= 216
    model.addConstr(11 * fruit_salads + 17 * cantaloupes <= 216, name="protein_upper_bound")

    # Fat upper bound: 1*fruit_salads + 21*cantaloupes <= 224
    model.addConstr(1 * fruit_salads + 21 * cantaloupes <= 224, name="fat_upper_bound")

    # Solve the model
    model.optimize()

    # Print the solution
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: fruit_salads = {fruit_salads.varValue}, cantaloupes = {cantaloupes.varValue}")
        print(f"Objective: {model.objVal}")
    else:
        print("The model is infeasible")

optimize_fruit_salads_and_cantaloupes()
```