3.3 A bottling company uses two inputs to produce bottles of the soft drink Sludge: bottling machines

(K) and workers (L). The isoquants have the usual smooth shape. The machine costs $1,000 per day to run. The workers earn $200 per day. At the current level of production, the marginal product of the machine is an additional 200 bottles per day, and the marginal product of labor is 50 more bottles per day. Is this firm producing at minimum cost? If it is minimizing cost, explain why. If it is not minimizing cost, explain how the firm should change the ratio of inputs it uses to lower its cost.

(Hint: Examine the conditions for minimizing cost:

Equations 7.5 or 7.8. See Solved Problem 7.3.)