Please help solve the attached question with steps. Thank you~

4. [30 POINTS] A rm has a production function y = f (L, K) = LIMP/3 where input prices are 111;. = $4 and 10K = 8. (a) [5 POINTS] Graph the rm's isoquant corresponding to its output of y = 100. What is the technical rate of substitution (TRS) at the point (L, K) = (4,10). Is L = 4, K = 10 is a cost minimizing bundle? Explain your answer. (1)) [10 POINTS] In short-run, if the quantity of capital xed, i.e.K = X. What is the rm's short-run total cost function as a. function of I? and y? (c) [5 POINTS] What is its short run marginal cost function? What is its short run average cost function? ((1) [10 POINTS] Calculate the rm's conditional demands for capital and for labor, given that it produces some level of y in the long-run by using the Lagrangian method. Find the rm's long-run cost function