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4. [30 POINTS] A rm has a production function y = f (L. K) = LINK\" where input prices are nu, = $4 and um = 8. (a) [5 POINTS] Graph the lm's ieoquant 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. (b) [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 K and y? (c) [5 POINTS] What is its short. run marginal cost function? What. is its short run average oust function? (d) [10 POINTS] Calculate the rm '5 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