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