Laura owns a pie company. She has learned that her profits, p(x), from the sale of x cases of pies are given by p(x)= 150x – x^2. (a) How many cases of pies should she sell in order to maximize profit

(a) In order to maximize profit, we need to find the critical point of the function p(x). We can do this by taking the derivative of p(x) and setting it equal to zero: p'(x) = 150 - 2x = 0 Solving for x, we get: x = 75 So Laura should sell 75 cases of pies in order to maximize profit. (b) To find the maximum profit, we need to plug x = 75 into the original profit function: p(75) = 150(75) - (75)^2 = 5625 Therefore, the maximum profit Laura can make is $5,625.