A business with technology can be described by the production function y = 4z1^1/2 + 2z2^1/2 . Assume that input 2 is fixed in the short run: z2 = 9. Also assume that the firm faces output price p = 6 and input prices w1 = 2 and w2 = 6.
(a) Solve for the firm’s (short-run) profit-maximizing choice of input 1 (z1) and output (y).
(b) Sketch an appropriate graph illustrating this optimal production choice.