E-Systems, a high-tech IT company, has the following production function: Q (L, K) = (VL + VK)2 , where L is the weekly labour hour, K is machinery used, and Q is the quantity of manufactured computer chip. The marginal product of labour and marginal product of capital are: MPL = (VL + VK)L-2, MPk = (VL + VK)K-2. The hourly wage, w, is t20, and the rental rate for the machinery, r, is f10. (a) What kind of returns to scale does E-System's production function exhibit? Explain your answer. (b) Calculate the rate of technical substitution of L for K, MRTSik. (c) In the short-run, E-Systems can rent only 4 pieces of machinery. How many labour hours is needed to produce 36 computer chips? (d) What is the cost of producing 36 chips? (e) What is the long-run optimal choices of labour and machinery to minimize the cost of producing 100 computer chips