Sylvia and Koichiro are starting a new high-volume Sushi restaurant, called Robo Sushi in Davis. While Koichiro plans to manage the business himself, he requires to employ some combination of workers and sushi-bots" to produce the sushi. He calculates 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 amortized cost of sushi-bots is equivalent to $40/hr.
1. Koichiro wants to form maximum number of sushi-rolls possible while spending no more than $3,000/hr. using the substitution method, what combination of Sushi-bots and Labor should he employ to maximize his output? Determine how many sushi rolls can he make?
2. Assume 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. Determine his short-run marginal cost of sushi?