Suppose a profit-maximizing firm produces output q, selling it for a price of $20 per unit regardless of what the firm does. In other words, the firm does not have any market power over its output price. In the short-run, the firm has to pay $50 dollars for its installations, regardless of how much it sells. Furthermore, its variable costs may be represented 0.1q2 + 109. (a) Write an expression for this firm's total costs, as a function of output. (b) Write an expression for this firm's marginal costs, as a function of output. (c) What amount of output should this firm produce? Do not forget to consider the possible scenario in which the firm may choose q = 0