Question: 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 = X²+ 2Y² – 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 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 average 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 answers.

(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.