Consider the following system of inverse demand functions: pA = 120 4qA 2qB and pB = 120 4qB 2qA. Assume that firms A and B do not bear any production costs (that is, cA = cB = 0). Solve the following problems: a) Suppose the firms compete in quantities, where firm A sets qA and firm B sets qB, simultaneously. Formulate the profit function of each firm as a function of the quantity supplied by both firms. Formally, write down and spell out the exact equations of each firm's maximization problem. b) Solve for the firms' quantity best-response functions qA = RA(qB) and qB = RB(qA). Plot both best-response functions where you denote the vertical axis by qA and the horizontal axis by qB. Indicate whether these best-response functions are upward or downward sloping. c) Solve for the Nash equilibrium quantity levels, qA and qB, the corresponding prices, pA and pB, as well as the equilibrium profit levels, A and B