Kindly solve showing each step

c) Suppose that there is a 40% chance the wage will rise to $15 What are the new short-run profit maximizing inputs, output, and the associated profit?5. Jorge has an idea for a new product to help Econ 3101 students graph 3 dimensional functions (like utility functions and production functions!). Jorge has figured out that to produce these devices, he needs capital and labor according to the following production function: F(K,L) = 15K^3/5L^2/5 (a) For now assume flexible capital and labor. Identify the elasticity of substitution for Jorge's production function. (2 points) (b) Suppose in the short run he can only get 2 units of capital. Set up and solve the cost minimization problem for Jorge's product in the short run. What are the short run values for inputs and what is the short run minimized cost? (4 points) (c) Suppose Jorge realizes that Econ 3101 students are very interested in his product because it helps them with the problem sets. All the student interest makes Jorge consider producing the product for the long run. Let capital and labor both freely move. Setup and solve the long run cost minimization problem for the optimal level of capital, labor, and the minimized cost.3. Consider a competitive firm which uses three inputs K (capital), L (labor), and A (land) to produce output y. The input prices are (wk = 2, wL - 1, wx = 4) and the output price is p = 1. The firm faces the following production function: f (K, L, A) = A ( VL + VK). In the short-run, the firm's land level is fixed at A, but can choose labor and capital as it wishes. In the long-run, the firm can also vary its land level. First, derive the short-run cost function given A. Then, use the short-run cost function to derive the long-run cost function. Hint: Use an approach similar to the example in class, where the profit-maximization problem can be decomposed into two steps. Here try to decompose the long-run cost minimization problem into two steps.]Problem 2 (20 Points) The production of Florida oranges uses two inputs: labor (L) and capital (K). The following production function describes how these inputs are combined to produce bushels of oranges. f(L, K) = 421/2 K a) Determine what kind of returns to scale this production function exhibits and the technical rate of substitution (HINT: labor is the "x" variable - the one that goes on the horizontal axis). b) Suppose the price of a bushel of oranges is $20, the wage is $5, and the rental rate is $8. In the short-run, capital is fixed at 10 units. Find the short-run profit maximizing inputs, output, and the associated profit