(30pts) Suppose the cookie factory use two inputs to produced cookies according to a production function given by: (1 , 2 ) = 21 + 2 . Cookies sell at $50 per crate. Input 1 costs $5 per unit and input 2 costs $50. a. If input 2 is fixed at 2 = 10, find the profit maximizing level of 1 . b. What is profit level enjoyed by the factory base on the result from part a? c. Now this factory free to vary its usage of all inputs. What is the profit maximizing level of 1? Any difference?