5. A recent Duke graduate has opened a factory for production of textbooks in Durham. The production function is as follows f«(K;L) = K L1/3 Currently, she uses K = 2000 and L = 500 and the rental rates of capital and labor are w=r=$1. Now she is considering expanding her business and opening another factory in Chapel Hill. Using her microeconomic skills, she estimates that the cost function for the factory in Chapel Hill will be C(q) = q2 The firm is facing a competitive market and the price at which it can sell its output is p = $30. a. Suppose that in the short-run, both inputs in the Durham factory are fixed. What would be the profit maximizing output in the Chapel Hill factory? What would be the total output QsR of the firm? Calculate the profit SRthat the firm will make in the short run. b. In the long run, both capital and labor are adjustable. Find the long-run cost function C(q) for the factory in Durham. c. Suppose that the firm wants to produce Q units in total from the two factories in the long-run. How should production be allocated between the two factories in order to minimize the cost of production? Find the total cost CLR(Q) associated with this allocation.