please answer those question

Question 6 {15 points] Bl. A perfectly competitive rm has a production function given by Q = L1I3K1f3. where q is output, L is labour and K is capital. (a) Derive the conditional input demand functions of the rm. (b) Derive the long-run total cost function for the rm. Sketch the long run cost curve. labelling at least three point on it assuming the wage rate is 25 and the rental rate is 64. (c) In the short-run, the rm uses 3 units of capital. Derive the rm's short-run demand for labour and its short-run total cost function. Given a product price of P, derive the short-run supply function of the rm