Patriots Inc. is a price-taking firm that produces Tricorns. Its short run cost function is c(y) = 5 + (y−3)3 30 . a) Derive the following functions for Patriots Inc.: i) fixed cost ii) variable cost iii) average total cost iv) average fixed cost 1 v) average variable cost vi) marginal cost b) Graph these functions on a graph with y on the x-axis and dollars on the y-axis. c) Suppose the market price for Tricorns is $10. How many Tricorns should Patriots Inc. produce to maximize profits? How much will it earn in profits?