The management of the producers of a famous hot sauce estimate that their profit (in dollars) from the daily production and sale of x cases (each case consisting of 24 bottles) of the hot sauce is given by P(x) = -0.0004x³ + 12x - 20 (a) How many cases of the daily production and sale should be to make the largest possible profit? Round your answer to the nearest integer, if necessary. You MUST justify that your result is an optimal value. (b)What is the largest possible profit the producers can make in 1 day? Round your answer to the nearest whole dollar.