In your answers, label all intercepts, coordinates, slopes, and axes. The output of a factory is described by the production function f (x1, x2) = 9,3/x1x2 1. Does input 361 exhibit the Law of Diminishing returns? What about input x2? Explain. 2. What kind of returns to scale does this production function exhibit? Explain. 3. What is the slope of the isoquant through the input combination (8, 5) ? Show your work. Given an English interpretation of the slope. Suppose the first input cost $ 15 per unit and the second 53 10 per unit. The market price for the output (in the perfectly competitive industry) is $12. 4. Assume that the amount of the second input is fixed at 5 units in the short run. Compute the profits of this firm if it chooses the optimal production technology in the short run. Show your work. 5. Compute the profits of this firm if it chooses the optimal production technology in the long run (when x2 is no longer fixed). Show your work. 6. Derive the cost function, using the technique of cost minimization, for this firm. Show your work