Koichiro and Sylvia are starting a new high-volume Sushi restaurant, called Robo Sushi in Davis. While Koichiro plans to manage the business himself, he needs to employ some combination of workers and \sushi-bots" (sushi-making robots) to produce the sushi. He estimates his production function as q = 10(L^0.5)K where q is the number of Sushi rolls, L is worker hours and K is sushi-bot hours. Workers cost $10/hour and the amortized cost of sushi-bots is equivalent to $40/hr.
(a) Koichiro wants to produce the maximum number of sushi-rolls possible while spending no more than $3,000/hr. Using the substitution method, what combi-nation of Labor and Sushi-bots should he employ to maximize his output? How many sushi rolls can he make?
(b) Suppose that a surge in lunch-time demand forces Koichiro to increase his output of Sushi quickly. He can only add worker-hours, and does not have time to add sushi-bots. What is his short-run marginal cost of sushi?