Exercise 2. 2.1) Let the following nut production function in a month be f(K, L) = 1000(VK + \\[ ) where K is the number of machines used and L is the number of workers working normal hours. Which of the following production plans are technologically possible? alProduce 10,000 nuts per month using 25 machines and 100 workers. biProduce 240,000 nuts per month using 25 machines and 81 workers. c)Produce 39,000 nuts per quarter using 25 machines and 100 workers. d) Produce 300 nuts per day (1 month = 30 days) using 9 machines and 36 workers e) Produce 5,000 puts per month using 0 machines and 36 workers. f)Produce 12,500 nuts per month using 36 machines and 36 workers. 2.2-a) explain graphically showing the production function with respect to the number of workers when the number of machines is fixed and equal to 25. 2.2 b) Represent in another graphically explanation for the production function with respect to the number of machines when the number of workers is fixed and equal to 36. 2.2 c) Place each of the six previous production plans in the graphically that you think is convenient to explain 2.2 d) If we consider that a production plan is efficient when the factors of production are not wasted (the maximum that can be produced for that plan is produced), determine which of the previous production plans are not only efficient, but also possible. 3. Assume the following production function for good X: X = 25L1/2K1/2 Where L and K are the labor and capital factors of production, respectively, used in the production process of X. a) Define the concept of isoquant, derive its equation and for this production function, derive the equation of these for the following production levels: X = 1000, 2000 and 3000 units of product (Hint: clear K). b) Define the concept of isocosts and derive its equation (Remember that CT = wL + [K). If the prices of the factors K and L, are w=$1 and r=$5,333, respectively, derive mathematically and graphically the isocost curve. c) Calculate and graphically the choice of the optimal combination of production factors and calculate the benefits considering that Py = $0.50 for the following cases of the company's benefits: d) Cost minimization for a production level of X = 3000. d.2 Production maximization subject to cost = $554.25