1. (16 pts) Suppose a prestigious U.S. university aims to produce two (2) highly specialized PhD students in nanochemistry every year. To produce nanochemistry PhDs requires two inputs: Lab time (L) and Nobel Prize-winning professors (N). 1 3 Suppose that the production function for PhDs is given by Y = L 4 N 4 where Y is the number of PhD students they produce a year. The marginal products of Lab time and of Nobel professors are given in the table below, along with their factor prices: 1 MPLA MPNR Price of L (in $ Price of N (in $ millions)a millions) ?x 0.42 1.20 (a) (10 pts) What are the cost-minimizing amounts of L and N for producing two PhD students a year? (Give some details for how you arrived at this.) 1 (b) (6 pts) What is the average cost of producing the two PhD students? 1