The following cost function represents your nail salon, which operates in a competitive market. () = 3³ 18² + 50 + 50, where is pedicures offered per day.

a. Derive your average fixed cost (AFC), average variable cost (AVC), average total cost (ATC) and marginal cost (MC) functions.

b. Illustrate the cost curves from (a) on a graph.

c. Calculate the minimum ordered pair of the AVC function using calculus (hint: same process for calculating min ATC). Make sure you label the minimum point of the AVC function on your graph.