12. Find the first and second derivatives of the following functions (a (b) (C) (d) (e) 13. Given the demand schedule P = 120 - 30 derive a function for MR. and find the output at which TR is a maximum. 14. For the demand schedule P= 40 -0.50 find the value of MR. when ? = 15. 15. Find the output at which MR is zero when P = 720-40 describes the demand schedule. 16. A firm knows that the demand function for its output is p = 400 - 0.5q. What price should it charge to maximize sales revenue? 17. If TC = 65 + qu what is MC when q = 25? 18. Derive a formula for MC if TC = 4q3 - 20q2 + 60q + 40. 19. If TC = 0.5q' - 3q2 + 25q + 20 derive functions for: (a) MC, and (b) AC 20. A monopoly faces the following TR. and TC schedules: TR = 300q- 2q2 TC = 12q3- 44q- + 60q + 30 What output should it sell to maximize profit? 21. A firm faces the demand function p = 190 - 0.6q and the total cost function TC = 40 + 30q + 0.4q- (a) What output will maximize profit? (b) What output will maximize total revenue? (c) What will the output be if the firm makes a profit of P4, 760? 22. A firm faces the total revenue schedule TR = 600q - 0.5q (a) What is the marginal revenue when q is 100? (b) When is the total revenue at its maximum? (c) What price should the firm charge to achieve this maximum TR? 23. For the non-linear demand schedule p = 750-0.1q- what output will maximize the sales revenue? 24. A firm's total revenue and total cost functions are TR = $2q - q' and TC= 4/3 -2.5q' + 34q + 4, at what output will profit be maximized? 25. A monopoly faces the total revenue schedule TR = 300q- 2q- and the total cost schedule TC =12q' - 44q"+ 60q + 30, Are there two output levels at which MC = MR? Which is the profit-maximizing output? 26. If a firm faces the demand schedule p = 120 - 3q and the total cost schedule IC = 120 + 36q + 1.2q' what output levels, if any, will (a) maximize profit, and (b) minimize profit? 27. What is the maximum profit a firm can make if it faces the demand schedule p = 660 - 3q and the total cost schedule TC = 25 + 240q - 72q + 6q? 28. If a firm faces the demand schedule p = 53.5 - 0.7q, what price will maximize profits if its total cost schedule is TC = 400 + 35q - 6q~+ 0.1