3. Assume that the manufacturing of generic medicine XYZ is a perfectly competitive industry. Suppose that the annual demand for this medicine is given by: Q = 1,450 - 30P. There are exactly a hundred manufacturers in the market. Each manufacturer has the same production costs. These are described by 5 total and marginal cost functions of: C(q)=2q2+ 25q + 2.5 and MC(q)=5q + 25. a. Show that an individual firm in this industry maximizes profit by producing: q=-5 + 0.2P. b. Derive the industry supply curve and show that it is: Q = -500 + 20P. c. Find the market price and aggregate quantity traded at the equilibrium price. d. How much output does each firm produce? e. Calculate each firm's profit. f. Using market demand and supply functions (Q, Q5): i 11. 111. Graphically represent the equilibrium in the market; Calculate producer surplus; and Consumer surplus in this competitive equilibrium.