A market's total demand is given by P = 40 - Z. This market is supplied by a "dominant firm" and by other, relatively small firms. The small firms'...

A market's total demand is given by P = 40 - Z. This market is supplied by a "dominant firm" and by other, relatively small firms. The small firms' total supply is given by P = 3Y. The dominant firm's total-cost function is TC = (X2/8) + 2X + 3 [In case you have no calculus: Marginal Cost = MC = (X/4) + 2 ]. (a) Find the equation of the dominant firm's derived-demand function [Hint: READ THE RELEVANT COURSE NOTES on pp. 160-161 and proceed as follows: X = Z - Y]. (b) Find the equation of the dominant firm's Total Revenue (TR). (c) Calculate the dominant firm's output (X) and price (P) at its profit-maximizing equilibrium. [In case you have no calculus: MR = (120 - 6X )/4 ]