Hi, could you please help me on this question?

Consider a firm producing output, Q, using labour, L and capital, K as the two inputs, where the price of labour is w = 40 and the price of capital is 7 # 50. The firm's total costs are TC = $10,000. Assume that the production technology to produce the output is given by: Q = 20L + 30K (a) What will be the firm's optimal choice of inputs? Referring to marginal product and input prices, explain why this is the optimum point. (5 marks)Now consider a firm with the following production technology: Q = L1/4K'/* with the price of labour denoted by w and the price of capital denoted by r. (b) Set up the firm's long run profit maximisation problem and solve to find an expression for the firm's supply function and its profit function. (15 marks) (c) A firm's decision to produce, and how much to supply, depends on whether we consider the short run or the long run. Explain how a firm's average costs will be used when it is deciding when and how much to supply in the short and long run