"8. Given the following total-revenue and total-cost functions of a firm TR - 220 -0.50 TC = Q - 8.50 + 500 +90 determine (a) the level of output at which the firm maximizes its total prof. (b) the maximum profit that the firm could earn. 9. A firm's total-revenue and total-cost functions are TR = 40 TC = 0.04Q'-0.90+ 100+5 (a) Determine the best level of output. (b) Determine the total profit of the firm at its best level of output. 10. Given the following cost functions, determine the level of (nonzero) output at which the cost functions are minimized and the level of those costs. Ha (a) AC = 200 -240 + Q (6) MC = 200 -480 + 3Q' Ha *11. For the following total-profit function of a firm: 7 = 144X - 3X? - X) - 2Y + 1201 - 35 determine (a) the level of output of each commodity at which the firm maximizes Ro its total profit; (b) the value of the maximum amount of the total profit of the firm. 12. Integrating Problem The Warren & Smith Company manufactures commercial zippers of two kinds, kind X and kind Y. Its production department estimates that the average-cost function of the firm is AC = X3+ 21" - 2XY - 2X - 6Y + 20 (a) The manager of the firm would like to know the level of output of zipper X and zipper Y at which the average cost of the firm is minimized and the level of this minimum average cost. (b) The firm expects an order of both zippers that will require it to produce a total output of 6 units of both kinds of zippers (each unit may be a large number of zippers), and so the manager would also like to know how many of each type of zipper the firm must produce to minimize its av- erage cost, and what its minimum average cost would be if it receives the order. The manager gives this assignment to two researchers who use different methods to obtain their answer. (c) While the firm expects the order to be of 6 units, it may be as large as 7 units or as small as 5 units. Determine the minimum average cost of the firm with these different order sizes