## Problem Description and Formulation

The food truck optimization problem can be formulated as a linear programming problem. The goal is to maximize profit given certain constraints on the supply of tacos and burritos and the total number of items that can be cooked.

### Decision Variables

- \(x\): The number of tacos to sell.
- \(y\): The number of burritos to sell.

### Objective Function

The profit per taco is $3, and the profit per burrito is $6. The objective function to maximize profit (\(P\)) is:

\[ P = 3x + 6y \]

### Constraints

1. **Minimum Sales Requirements:**
   - At least 50 tacos: \( x \geq 50 \)
   - At least 30 burritos: \( y \geq 30 \)

2. **Supply Constraints:**
   - At most 80 tacos: \( x \leq 80 \)
   - At most 50 burritos: \( y \leq 50 \)

3. **Total Items Constraint:**
   - At most 100 items total: \( x + y \leq 100 \)

4. **Non-Negativity Constraints:**
   - \( x \geq 0 \) and \( y \geq 0 \), but these are partially covered by the minimum sales requirements.

## Gurobi Code

```python
import gurobi

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

    # Define the decision variables with their bounds
    x = model.addVar(lb=50, ub=80, name="tacos")  # At least 50, at most 80 tacos
    y = model.addVar(lb=30, ub=50, name="burritos")  # At least 30, at most 50 burritos

    # Add the constraint for the total number of items
    model.addConstr(x + y <= 100, name="total_items")

    # Define the objective function
    model.setObjective(3*x + 6*y, gurobi.GRB.MAXIMIZE)

    # Optimize the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.Status.OPTIMAL:
        # Get the optimized values
        tacos_to_sell = x.varValue
        burritos_to_sell = y.varValue
        max_profit = model.objVal

        print(f"Optimal Solution: Sell {tacos_to_sell} tacos and {burritos_to_sell} burritos.")
        print(f"Maximum Profit: ${max_profit:.2f}")
    else:
        print("The model is infeasible.")

# Run the optimization
food_truck_optimization()
```