4. A firm produces output, y, according to y = 32 x. It pays k for its input, x, and sells each unit of output for p. Assume x 0 (a) Write the firm's profit function, cost function, and revenue function. (b) Find the quantity of inputs that maximizes firm profits. (c) Use a first derivative test and sign diagram to check whether your answer in b is a maximum. (d) Does your profit function have an inflection point if x 0?