Please show all work and the graph for part C. Thank you!

d) Derive the long-run average cost curve and the long-run marginal cost curve. f) Derive the short-run average cost and the short-run marginal cost curves. e) Now consider the short-run scenario where capital is fixed. In this case K=4, derive the short-run cost curve. Use the following production function and marginal products to answer the parts of this question: Q=100L21K21MPL=50L21K21MPK=50L21K21 a) Find the input demand curves for both labor and capital. b) Derive the long-run total cost curve. c) Say the price for labor is w=100 and the price for capital is r=25. Plug in these values into the long-run total cost curve and graph it