3. A rrn's production function is Q = K \"-51.95, where K is capital input measured in machine hours and L is labour input measured in worker-hours- The rm is perfectly competitive and hires its machines at a constant rental rate of r = 4 per hour and its workers at a constant wage rate of w = 1 per hour. (a) Show that the minimum total cost of producing 100 units of output is 400, and that this is achieved by employing 50 machines and 200 workers. (b) Show that cost minimization requires employing capital and labour so as to make the ratio of marginal products, %, equal to the ratio of input prices, ;. (c) How does the minimum total cost of producing 200 units compare with that of producing 100 units? What does your answer tell us about the rm's total and average cost curves, as a function of Q? (d) In your solution to (a) above, you may have noticed that of the minimized total cost, 400, half of this is spent on hiring workers and half on hiring machines. Would this 50:50 split also occur if we had, say, w = 9 and r = 1