Suppose a firm uses both labour (L) and capital (K) as inputs and has the production function q = 2KL. The marginal product of labour is 2K. The marginal production of capital is 2L. If capital rents for $200 and labour can be hired for $100 per day and the firm is minimizing costs:
i) What is the total cost of producing q units of output? What is the average cost of producing q units of output?
What is the marginal cost of producing q units of output?
ii) What combination of capital and labour should it use to produce q = 64?
What would be the cost of production?