A small business that uses machines (K) and labour (L) to produce output (Q). Two workers for every machine, so the production function is Q = min{L, 2K}. The wages w = 25 for every unit of labour and r = 400 for every machine. Production of 6,000 units of output Q.

(a) Write down the long-run "producer's problem" [define the objective, any constraints and what is being chosen to achieve the objective.]

(b) What quantities of Labour and Captial are demanded?

(c) What is the minimized total cost?