1. (12 points) Suppose Restaurant A is a fast-food restaurant that sells burgers. Restaurant A can produce burgers by hiring workers (N) and/or renting automated machines (K). Assume that Restaurant A's production function is Q = 5 . (3N + K). The cost of hiring one worker is w and the cost of renting an automated burger machine is r. For simplicity, assume that the price of a burger is normalized to p=1. a) (3 points) Suppose w=1 and r=2. What is Restaurant A's cost-minimizing input choice (N*, K*) in order to produce Q=100? Explain. b) (3 points) Suppose w=1 as in part (a), but it becomes cheaper to rent machines such that 1=1. Conditional on Restaurant A producing Q-100, how would this affect Restaurant A's optimal (N*, K*)? Explain. c) (4 points) Conditional on maintaining the same total cost level as in part a), graphically illustrate the magnitude of the substitution and scale effects when the rental cost of machines decrease from 1=2 to r=1 (the wage rate is still the same at w=1). d) (2 points) Now assume that the price of hiring workers increases such that w=3 and r=1. What is Restaurant A's cost-minimizing input choice (N*, K*) in order to produce Q=100? Explain