Kindly work out all the questions

c. Q=51"K - L 2. Using the production function from part c above, assume that capital is fixed at two units. At what point does MP reach zero? 3. Suppose a firm uses both labor (L) and capital (K) and its long run production function is given by the expression Q - F(L,K) - 12 X V(L + 2K). The firm currently uses 100 units of capital. Assuming labor is finely divisible, graph the firm's short run production function for the first five workers. 4. Suppose you manage a firm with two production plants. The marginal product of labor at plant 1 is MPI- 1400 - LI where LI is the number of workers employed in plant 1. The marginal product of labor at plant 2 is MP2 - 2000 -L.2 where L.2 is the number of workers employed in plant 2. Given that you have 1,000 workers, what is the best allocation of workers between the two plants?2. (a) Define, and carefully explain in your own words, what it means for [5] a function f : R - R to be differentiable at a point Xo E . (b) Plot the function f : R - R in a graph, where (10] f (x ) = |x -1| if x 5 2. if x > 2. (Recall |z) = z if z 2 0 and |z| = -z if z