Please help me get the answer and explanation to this question.

Question 3 3 A firm's production function is given by: F(L, K) = LX4 . You also know that the wage rate is $2, the price of capital is $6, and the price of the product is $216 a) In the short-run, capital is fixed at 1 unit. How many units of Labor (L) should this firm hire? b) How much profit is the firm making in the short-run? c) Assuming that in the long-run both capital (K) and labor (L) are variable inputs, what is the optimal combination (profit-maximizing/cost-minimizing _' and K' ) to produce the same amount of output as in the short-run? d) What are the profits in the long-run? e) Assume that the firm has a fixed cost of $200. Find the variable cost function, the total cost function, the marginal cost function, the average total cost function, the average fixed cost function, and the average variable cost function (hint: to answer this question, first, redo all calculations in part (c) in terms of a general level of output Q. In other words, first find L* and K* as a function of Q using the tangency condition, then find cost functions)