The production function for an automobile industry is given by Q = 2√(K)√(L), where Q is the number of automobiles produced per day, K is the number of machines, and L is the number of workers employed by the factory. Suppose that K is fixed at 100 and the rent for a unit of capital, r, is given by $20. Also, the wage for each worker, w, is $100. Find the total cost function.
TC = 2000 + Q^(1/2)/4
TC = 2000 + Q^(2/4)
TC = 2500 + Q^(1/2)/4
TC = 2500 + Q/2