## Problem Description and Formulation

The breakfast place needs to mix two pancake mixes, A and B, to achieve a final mixture that contains at least 10 kg of sugar and 50 kg of flour. Mix A contains 10% sugar and 60% flour, while Mix B contains 15% sugar and 50% flour. The cost per kg of Mix A is $20, and the cost per kg of Mix B is $25. The goal is to minimize the total cost.

## Mathematical Formulation

Let's denote the amount of Mix A to be bought as \(x_A\) kg and the amount of Mix B as \(x_B\) kg.

- The sugar content in Mix A is \(0.10x_A\) kg and in Mix B is \(0.15x_B\) kg. The total sugar content needs to be at least 10 kg:
  \[0.10x_A + 0.15x_B \geq 10\]

- The flour content in Mix A is \(0.60x_A\) kg and in Mix B is \(0.50x_B\) kg. The total flour content needs to be at least 50 kg:
  \[0.60x_A + 0.50x_B \geq 50\]

- The cost of Mix A is $20 per kg, and the cost of Mix B is $25 per kg. The total cost \(C\) to be minimized is:
  \[C = 20x_A + 25x_B\]

- Non-negativity constraints: \(x_A \geq 0\) and \(x_B \geq 0\), as the amounts of Mix A and Mix B cannot be negative.

## Gurobi Code

```python
import gurobi

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

    # Define variables
    x_A = m.addVar(name="Mix_A", lb=0)  # Amount of Mix A
    x_B = m.addVar(name="Mix_B", lb=0)  # Amount of Mix B

    # Objective function: Minimize cost
    m.setObjective(20 * x_A + 25 * x_B, gurobi.GRB.MINIMIZE)

    # Constraints
    m.addConstr(0.10 * x_A + 0.15 * x_B >= 10, name="Sugar_Requirement")
    m.addConstr(0.60 * x_A + 0.50 * x_B >= 50, name="Flour_Requirement")

    # Solve the problem
    m.optimize()

    # Check if the model is optimized
    if m.status == gurobi.GRB.OPTIMAL:
        print(f"Optimal amount of Mix A: {x_A.varValue} kg")
        print(f"Optimal amount of Mix B: {x_B.varValue} kg")
        print(f"Minimum cost: ${m.objVal:.2f}")
    else:
        print("The problem is infeasible.")

solve_pancake_mix_problem()
```