Question 5 (12 marks) A rm must fulll an order of 100 units of q. They can convert two inputs, K and L, into output via the production function F(K, L) = 101n (KL). Every unit of K that they use costs $10. Every unit of L costs $40. The rm wants to minimize their production costs subject to fullling the order. Based on the above information, answer the following questions. (a) What is the objective function that the rm is minimizing? (2 marks) (b) What is the constraint that the rm is facing? (2 marks) (0) Write down a Lagrangian that represents the rm's constrained optimization problem. (2 marks) (d) What is the optimal amount of K and L that the rm should use? Show that this is a global minimum. (6 marks)