The average cost (AC) curve cuts the marginal cost (MC) curve at which point of the AC curve?

Consider the following statements regarding the theories of cost in microeconomics: Statement 1: Traditional neoclassical cost theory derives smooth, U-shaped short-run average cost curves directly from the operation of the law of variable proportions. Statement 2: Modern cost theory argues that the long-run average cost (LAC) curve is U-shaped, indicating that diseconomies of scale are pervasive in manufacturing. Which of the statements given above is/are correct?

In the long-run theory of cost, the optimum scale of production is achieved where: