Question 3 (a) (b) (C) (d) A rm can produce a maximum of 1500 sport cars every year. If the producer sells q cars, then the prot is \"(q) = 30,000,000 360,000q + 750612 q3 in dollars. How many cars should the producer try to sell to maximize the prot? (5 marks) 3 Suppose a producer faces a nonlinear inverse demand function p = (650 0.2 Sq)? What is the amount of output q should it try to sell to maximize the total revenue? Use the second derivative test to conrm your result. (5 marks) . . . 30 Suppose the inverse demand lnction IS p -# m an p = q + 1. Calculate the consumer surplus. d the inverse supply function is (5 marks) Consider the supply is QS : 12 + P and the demand is Q\" = 32 P. Suppose the government imposes a 5% sales tax on the producers. Calculate the equilibrium price, equilibrium quantity, and price elasticity of demand at the equilibrium point. (5 marks) The marginal revenue function for a goods is M R(q) = 44 Sq. The marginal cost is M C (q) = 3q + 20, and cost of producing 100 units is $ 100,000. Derive the prot function and calculate the prot or loss from selling 200 units