1. The problem involves optimizing the location for Pizza Pronto's next distribution kitchen using an advanced linear programming model. 2. Linear programming is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. 3. The general form of a linear programming problem is: $$\text{Maximize or Minimize } Z = c_1x_1 + c_2x_2 + \cdots + c_nx_n$$ subject to constraints: $$a_{11}x_1 + a_{12}x_2 + \cdots + a_{1n}x_n \leq b_1$$ $$a_{21}x_1 + a_{22}x_2 + \cdots + a_{2n}x_n \leq b_2$$ $$\vdots$$ $$a_{m1}x_1 + a_{m2}x_2 + \cdots + a_{mn}x_n \leq b_m$$ and non-negativity constraints: $$x_i \geq 0, \quad i=1,2,\ldots,n$$ 4. Mr. Hamza's model likely includes variables representing potential locations, costs, and constraints such as budget, distance, and capacity. 5. The solution involves: - Defining decision variables (e.g., $x_i$ = 1 if location $i$ is chosen, 0 otherwise). - Formulating the objective function to minimize costs or maximize efficiency. - Applying constraints based on operational limits. 6. The linear programming model is solved using methods like the Simplex algorithm or software tools. 7. The optimal solution provides the best location choice for the new distribution kitchen ensuring operational efficiency and effectiveness. Final answer: The advanced linear programming model helps Mr. Hamza determine the optimal location for Pizza Pronto's next distribution kitchen by maximizing efficiency and meeting all operational constraints.