A firm has a production function, q = 2vkl, where q is daily output (in kilogram) and I and k are daily inputs of worker-hours and machine-hours respectively. In the short run, the firm's machine-hours is fixed at k = 100 hours. The rental rate for k is v = $3, and the wage rate for l is w = $12. (a) Derive the firm's short-run total cost (STC), short-run average cost (SAC), and short-run marginal cost (SMC) functions. (b) For the daily output of q = 200 kilograms, calculate the firm's STC, SAC and SMC. (c) Graph the SAC and SMC functions for the firm. Indicate the point corresponding to your answer in part (b). Comment on where the SMC curve intersects the SAC curve