## Problem Description and Formulation

The problem is a classic example of a linear programming problem. The taco stand wants to maximize its profit by selling fish and chicken tacos under certain constraints.

### Decision Variables

- Let \(x\) be the number of fish tacos sold.
- Let \(y\) be the number of chicken tacos sold.

### Objective Function

The profit per fish taco is $6, and the profit per chicken taco is $4. The objective is to maximize the total profit \(P\), which can be represented as:

\[P = 6x + 4y\]

### Constraints

1. **Minimum Sales Requirements:**
   - At least 20 fish tacos: \(x \geq 20\)
   - At least 40 chicken tacos: \(y \geq 40\)

2. **Maximum Production Capacities:**
   - At most 50 fish tacos: \(x \leq 50\)
   - At most 60 chicken tacos: \(y \leq 60\)

3. **Total Production Limit:**
   - At most 80 tacos in total: \(x + y \leq 80\)

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

## Gurobi Code Formulation

Given the problem formulation, we can now translate it into Gurobi code in Python:

```python
import gurobi

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

    # Define variables
    x = model.addVar(lb=20, ub=50, name="fish_tacos")  # At least 20, at most 50
    y = model.addVar(lb=40, ub=60, name="chicken_tacos")  # At least 40, at most 60

    # Objective function: Maximize profit
    model.setObjective(6 * x + 4 * y, gurobi.GRB.MAXIMIZE)

    # Additional constraint: Total tacos cannot exceed 80
    model.addConstraint(x + y <= 80, name="total_tacos")

    # Solve the model
    model.optimize()

    # Check if the model is optimized
    if model.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal solution: Fish tacos = {x.varValue}, Chicken tacos = {y.varValue}")
        print(f"Maximum profit: ${6 * x.varValue + 4 * y.varValue}")
    else:
        print("The model is infeasible.")

solve_taco_stand_problem()
```

This code sets up the optimization problem with Gurobi, solves it, and prints out the optimal number of fish and chicken tacos to sell in order to maximize profit, along with the maximum achievable profit. If no optimal solution exists (i.e., the problem is infeasible), it will indicate that.